Having raised a complete generation of this species, I now feel confident to share my methods.
Enclosures
The most important factor is the enclosure. They need high humidity, and I have been able to achieve this with planted enclosures. The specific enclosure that seems to be ideal is a modified Styrofoam ice chest. My first one (covered in the Spring Collection Update) was a bit overly complicated, and I have experienced continuous issues with the glass door. This season I began experimenting with new, more streamlined designs. I replaced the light bulb with LED light strips, which allowed me to customize the wiring. Custom wiring led to the decision to connect the circuit through a hole in the side of the enclosure instead of making the hole in the top of the lid. Now these tanks are stackable. I have also come to the conclusion that pure perlite is probably safe enough for mantis tanks. It is a rather inert material and should not present much of a risk of being consumed by feeder insects. The addition of perlite will greatly improve the health of the plants in the vivarium. Finally, I have been focusing on just making the bottom of the tank waterproof and forgoing the liner. Some Styrofoams seem denser than others, and these types are more water resistant. For the record, though, these tanks are not intended to hold more than a cup or so of liquid water; the main concern is containing the water in the moist soil needed to grow plants. I do address the possibility of other enclosures later on, but my best results so far have been exclusively with foam tanks.
Feeding
While indubitably important, I have classified this as less important than the enclosure considerations because these mantids are quite the generalist predators. I have seen some warn that Brunneria borealis nymphs need special, small prey items, such as springtails, to eat because they are too delicate when they hatch. Fortunately, this is not the case, and the newborn nymphs can easily tackle a D. hydei fruit fly. The first three instars can usually continue to eat the hydei, but other foods are able to be used as well. Small roaches (I used red runners [Blatta lateralis]) can be fed to L3s and older. Select food that is about half the length of the mantis, and be aware that roaches, crickets, mealworms, and some others can chew through Styrofoam if left in the tank for more than a few hours. Hand-feeding is best when using these prey items, and it also prevents leftover prey items from stressing the mantis. The best prey item in my opinion are moths. I have reared armyworms in the past, and both the caterpillars and the moths were an excellent food source. Wild moths can be risky due to pesticides and infections, however, I have personally used wild moths as well for adults with no ill effects, despite living in a pesticide-rich suburban neighborhood.
First proof I saw that hatchlings are fine with D. melanogaster fruit flies. 
I then found the hatchlings handling the larger D. hydei just fine. 
The adults were the right size for subadult Blatta lateralis. 
Their favorite, though, is moths, as Arwen is demonstrating here.
Plants
Now I have stated that they benefit from planted enclosures. When setting up my enclosures, I chose to take inspiration from a common name of this species: the northern grass mantis. I specifically have been planting sorghum and zoysia grass in the enclosure. Both of these can be obtained in bulk, the sorghum as a specialty grain, and the zoysia grass at a garden or hardware store. I am sure that plenty of other plants will work. The rationale for these two species was that I already had them, and I found that they sprouted very quickly. Also, these seeds hold their viability for a long period of time.
The original tank had sorghum and spanish moss (Tillandsia usneoides) the first season. 
The 92˚F tank has a mix of zoysia and sorghum. 
The newest completed tank has exclusively sorghum as it is smaller than the other two.
Temperatures
With the original Styrofoam enclosure, the insulating properties of said foam allowed the temperature to reach about 85˚F during the day just using the heat from the 9-watt grow light bulb. At night, the temperature would gradually fall to about 70˚F, equal to the ambient room temperature. One of my new tanks reaches around 92˚F, and while this daytime temperature should be fine for this species, I plan to increase ventilation anyway. In general, I recommend keeping temperatures for nymphs between 65˚F and 90˚F.
Oothecae Incubation Temperatures
Hibernation is optional for this species. I have successfully hatched oothecae that were kept at about 70˚F all winter. Without hibernation, one ootheca I tracked took 176 days to hatch.
To hibernate an ootheca of this species, place the ootheca in a container with a humidity source, such as a wet paper towel, in the fridge but keep it above 35˚F for several months. During this period, do not allow the aforementioned humidity source to dry out, and make sure the ootheca is not in direct contact with moist surfaces or materials for prolonged periods to avoid causing the ootheca to rot.
I have noticed that these oothecae seem to have a propensity to grow a wispy mold at times. I have not noticed this to be a problem, however, and I still see nymphs hatch from ootheca that exhibited this mold.
Humidity and Ventilation
Humidity needs to be high for the nymphs and adults. For comparison, I keep these at a much higher humidity level than when I reared my flower mantids long ago. I achieve this via the planted tanks and continuously moist substrate along with misting/watering every couple days. With dedication, it is likely possible to substitute daily misting for the planted enclosure. With very frequent misting, deli cups may be a suitable enclosure, although I have not personally had success with using them for Brunneria borealis.
Ventilation needs are relatively low in this species. My first Styrofoam tank had a mesh-covered hole totaling about two square inches of area. For a tank about a cubic foot in volume, this gives an estimate of about square inch of ventilation per half a cubic foot of tank volume. This is merely an observation of my own successes, though, so similar configurations are likely to work as well.
Photoperiods and Lighting
In my collection, all my Brunneria borealis tanks have a 16-hour day and an 8-hour night, year-round.
The lighting in tanks is primarily a mix of 4:1 red:blue SMD 5050 grow light LED strips and generic cool white (5000+K color temperature) LED strips. These are cut to fit the particular tank, the adhesive backing is used to affix them directly to the foam, and then I solder them in parallel to power all of the strips evenly. For wiring, I use 18-gauge wire, and the power supply provides a constant 12 volts. I have not had issues so far with overheating despite the foam mounting point being an insulator, however, make sure your setup does not become too hot or it will start to melt the foam or worse.
Time Periods and Growth Rate
Total time is recorded below, but these are likely highly variable observations. Still, they should be accurate within a few weeks.
- Oothecae incubation (room temp) ~ 175 days
- L1 to adult ~ 125 days
- Adult lifespan ~ 150 days