In a 2-quart saucepan cook leek or onion in hot margarine or butter until tender but not brown. Stir in fresh or dried thyme, salt, and pepper. Add milk all at once. Cook and stir over medium heat until the mixture is heated through.
Stir in ham or turkey, potato buds or flakes, and basil leaves, if desired. Cook and stir until the mixture is slightly thickened. If necessary, stir in additional milk to thin to desired consistency. Sprinkle each serving with cracked pepper. Makes 6 servings.