Melt the butter in a large, enameled cast-iron casserole. Add the onion and cook over low heat, stirring occasionally, until softened, about 5 minutes. Add the paprika, cayenne and a large pinch of pepper; cook for 1 minute, stirring. Add the mushrooms, cover and cook over moderate heat until softened, about 5 minutes. Uncover and cook, stirring, until browned, about 5 minutes longer. Stir in the remaining 3 tablespoons of flour and gradually stir in the stock until smooth.