Heat the oil in a skillet over medium heat. Cook and stir the mushrooms, onion, and garlic in the hot oil until browned, about 5 minutes; set aside.
Melt the butter in a pot over medium-high heat. Add the quinoa to the melted butter and let it brown, about 3 minutes. Pour the chicken broth over the quinoa; bring to a boil. Cover and reduce heat to low; simmer 10 minutes. Stir in the sauteed mushroom mixture and cook another 2 minutes. Sprinkle with Parmesan cheese to serve.