Saute onion in butter in a heavy skillet until onion is tender; discard onion. Cook butter over low heat until it begins to brown. Add flour, stirring until smooth ( I find that a whisk works best). Cook 1 minute, stirring constantly. Add bouillon granules, and gradually stir in water. Cook over medium heat, stirring constantly, until thickened and bubbly. Stir in pepper. Serve with beef or pork.
Bordelaise Sauce: Substitute 1/3 cup dry red wine for 1/3 cup of the water, and stir in 3/4 teaspoon dried parsley flakes and 1/4 teaspoon dried whole thyme; increase pepper to 1/4 teaspoon.
Mushroom Brown Sauce: Saute 1/2 cup sliced mushrooms in 2 tablespoons butter; drain and stir into Basic Brown Sauce. Serve with beef.