Melt 2 tablespoons of butter in a saucepan over medium heat. Add the mushrooms to the saucepan and cook until the mushrooms are tender, stirring constantly. Remove the mushrooms and set aside.
Melt the remaining 1 tablespoon of butter in the saucepan. Add the minced garlic and cook for 1 minute. Stir in the flour and cook, stirring, for 1 minute. Add the beef stock, beer, and thyme. Continue cooking until thickened, stirring constantly.
Add the mushrooms back to the saucepan and bring to a simmer.