Spray both sides of mushrooms and place them bottom down on a rimmed baking sheet. Sprinkle the tops with salt and pepper. Bake for 10 minutes.
While the mushrooms are baking, cook the quinoa according to package directions. Once it's finished cooking, stir in the tomato sauce, garlic, basil, oregano, onion powder, and pepper flakes. Season to taste with salt and pepper.
After 10 minutes, remove the baking sheet from the oven and flip the mushrooms over. If they fill up with liquid (sometimes they do), drain it off or blot them dry with paper towels.
Divide the quinoa mixture into the mushrooms, then top each one with cheese. Return the baking sheet to the oven and bake for 10 minutes more. You can serve the mushrooms after this or turn on the broiler and broil them until the cheese is browned—about 3–5 minutes (just keep an eye on them so they don't burn!).