Melt the butter in a medium saucepan over medium-low heat; add the shallot and garlic and cook for about 5 minutes, or until the shallot is tender.
Add the flour to the shallot mixture and continue to cook for 4 minutes, stirring frequently. Add the beef broth, wine, Worcestershire sauce, and bay leaf. Simmer over low heat until the flavors are concentrated and the sauce is thick, about 45 minutes to 1 hour. Stir occasionally to prevent scorching.