Preheat the oven to 400F degrees.
Bring 3 Tablespoons quinoa and 6 Tablespoons water to a boil in a small saucepan. Cover, reduce to a simmer and cook for 10 minutes. Turn the heat off and leave the covered saucepan on the burner for another 4 minutes. Fluff with a fork and allow the quinoa to cool.
Gently twist mushroom stems to remove them. Finely dice the stems. Melt ¼ cup butter or olive oil in a small saucepan and sauté the stems and ¼ cup onion on medium heat until the onion is opaque and tender, 3 to 5 minutes. Remove from the heat and allow to cool.
Stir the quinoa, ¼ cup pistachios, 3 Tablespoons parsley, ¼ teaspoon oregano, ½ teaspoon pepper sauce, ½ teaspoon salt and 2 Tablespoons of freshly grated Parmesan cheese into the mushroom and onion mixture. Using a teaspoon, scoop the filling into the mushroom caps and place them on a baking sheet. (They can be refrigerated at this point for up to 24 hours.)
Bake for 13-15 minutes, depending on their size, until the mushrooms are tender. Sprinkle with remaining Parmesan cheese. Add a dash of red pepper flakes, if desired. Serve warm.