Preheat the oven to 400 degrees. Line a rimmed baking sheet with aluminum foil, then set an oven-safe cooling rack inside the baking sheet. Grease lightly with olive oil.
In a large bowl, combine all ingredients for filling (quinoa through black beans). Mix until combined.
Lightly brush mushrooms with olive oil, then bake for about 10 minutes, until slightly tender.
Remove from the oven, but do not turn off oven.
Place a large mound of the filling into each of the mushrooms, then sprinkle each with some of the vegan cheese. Return to the oven and bake for an additional 5 minutes, or until the cheese is melted.
Serve with avocado and cilantro on top.