Preheat the oven to 400 degrees F. Oil a rimmed baking sheet.
Heat the 2 teaspoons oil in a large skillet over medium heat and cook the onions and garlic, stirring often, until the onions are soft, about 3 minutes. Add the mushrooms, cumin, salt and green chiles. Cook, stirring occasionally, until the mushrooms are soft, 3 to 4 minutes.
Transfer the mushroom mixture to a large bowl and add both beans, tomatoes, brown rice, cheese, the 1 cup salsa and 1/2 cup cilantro. Stir to combine the filling.
Place 3/4 to 1 cup of the filling in the center of each tortilla and fold the sides in. Then fold the bottom up to cover the filling and fold the top down.
Place the chimichangas, seam-side down, on the prepared baking sheet and brush or spray them lightly with oil. Bake until the tortillas are golden brown, about 15 minutes. Serve with sliced avocado, sour cream, extra salsa and cilantro.
If the tortillas are too stiff to fold, microwave them for 30 seconds between 2 damp paper towels to soften.