Finely chop the onion and mince the garlic.
In a medium saucepan, melt the butter over medium heat.
Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic and sauté for an additional 1-2 minutes.
Sprinkle the flour over the sautéed onions and garlic.
Stir continuously with a whisk for about 2 minutes to form a roux, which will thicken the sauce.
Gradually pour in the beef broth while whisking to prevent lumps.
If using, add the red wine for extra depth of flavor.
Add the Worcestershire sauce, salt, and pepper to taste.
If desired, add fresh thyme or rosemary sprigs.
Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes, stirring occasionally.
Remove the thyme or rosemary sprigs.
Pour the Au Jus through a fine mesh strainer into a serving bowl to remove any solids.
Serve hot alongside your roast beef or any other meat dish.