Heat butter and olive oil in a skillet over medium heat.
Add sliced mushrooms and sauté until golden brown, about 5-7 minutes.
Stir in minced garlic and cook for an additional minute.
Sprinkle flour over the mushrooms, stirring to combine.
Cook for 1-2 minutes to eliminate the raw flour taste.
Gradually add broth while continuously stirring to avoid lumps.
Bring to a simmer and cook until thickened, about 3-5 minutes.
Stir in soy sauce and Worcestershire sauce for added flavor.
Season with salt, pepper, and thyme to taste.
Serve hot over your favorite dish.