Preheat oven to 400°F (200°C).
Place 1 tsp of olive oil in a small sauce pan over medium heat. Add the black beans, water, cumin, and oregano. Bring to a simmer.
Using a fork or potato masher, mash the black beans as they cook. As the beans are simmering, add additional water if needed to keep the beans from drying out. Simmer until beans become thick, about 15 minutes. When beans have thickened, remove from the heat and add the cilantro. Set aside.
In a medium bowl toss together the peppers, onions, garlic, mushrooms, salt, and pepper.
While beans are cooking, heat 1 tsp of oil in a saute pan over medium-high heat. Add vegetable mixture and cook until vegetables are soft, about 4 minutes.
Once the vegetables are soft, fold them into the bean mixture.
To assemble the tortillas, lay out 6 tortillas on a flat surface. Top each tortilla with 1 1/2 teaspoons of cheese, then 1/2 cup of the bean mixture, followed by another 1 1/2 teaspoons of cheese. Top each with another tortilla.
Place quesadillas in a single layer on a sheet tray. Bake in oven until cheese is melted and outside is crisp, about 5-8 minutes.
