Preheat oven to 375° F. Prepare a baking sheet covered in parchment paper. Add the black beans to the baking sheet in an even layer. Pat dry with a few paper towels. Bake for 18-20 minutes or until beans are steaming and starting to dry out (with no water/moisture on the pan). Remove pan and increase oven to 425° F.
Meanwhile (waiting for the beans to cook), prepare your flax egg (see below for tips*). In a small bowl, combine 2 tablespoons ground flaxseed and 3 tablespoons water. Stir and let sit for at least 5 minutes.
If you haven't already, chop the mushrooms and onion (diced very fine), and cut the tomatoes.
You can also make the aioli at this time. To do this, combine the mayo and Sriracha in a small bowl. Keep refrigerated until serving.
Add vegetable broth to a medium/large nonstick skillet or pot over medium high heat and add garlic, Cook for 30 seconds, stirring, then add mushrooms and onion. Cook for 2-3 minutes, stirring occasionally, until the mushrooms and onion are softened. Remove from heat and drain out any liquid if there is any.
In the same pot (no heat), stir in the soy sauce, pepper, breadcrumbs and flax egg until combined.
When the black beans are ready, add the dried black beans to the pot. To do this, pick up both sides of the parchment paper carefully and transfer the beans by first shaking and then using a spatula to remove the beans that may stick to the paper. Save the parchment paper if desired (you'll use it again later).
Lightly mash the beans in the pot using a potato masher. You want some of the beans whole/halved; don't over-mash. Once the beans are mashed, stir in the other ingredients with the beans until combined thoroughly.
Divide mixture into 6 equal portions and shape into patties. To divide portions evenly, you can use your fingers to carve out 6 sections in the bowl (see photo above in recipe instructions).
Arrange patties on a baking sheet covered in parchment paper, spaced out so they are not touching. Let rest for about 5 minutes, making sure the ingredients have time to bind together, then bake at 425° for 12 minutes. Flip the burgers and cook for another 12 minutes. They are done with they are firm and starting to brown. Remove from oven and let sit for 5 minutes.
To assemble, toast the hamburger buns, and top each bun half with a burger patty, 2-3 tomato slices, 1 tablespoon aioli sauce, a handful of arugula, and the remaining top halves of the buns. Serve with chips, sweet potato french fries or a small salad.