In a 4-1/2-quart Dutch oven combine cooking oil, flour, and margarine or butter. Cook and stir over medium heat until golden brown.
Stir in mushrooms, onion, dried thyme, salt, and pepper. Cook and stir until onion is tender. Combine beef broth and cornstarch; add to mushroom mixture along with milk, half-and-half, or light cream. Cook and stir until thickened and bubbly; cook 2 minutes more.
Divide into three 2-2/3 cup portions in freezer containers. Use immediately or seal, label, and freeze. Use as needed, thawing first.
To thaw, transfer a portion to a microwave-safe bowl. Microcook, uncovered, on 30 percent power (medium-low) 8 to 12 minutes; stir once. Or let one portion thaw overnight in the refrigerator. Makes about 8 cups sauce.