Melt the butter in a large skillet over medium heat.
Add the onion and mushrooms and cook until tender, about 10-15 minutes, stirring occasionally.
Add the minced garlic and sauté for 30 seconds.
Add the flour and stir to coat the vegetables. Sauté for two minutes.
Whisk in the beef broth, red wine and thyme.
Bring the liquid to a boil, then reduce the heat to medium low and simmer until the sauce begins to thicken, about 10-15 minutes more, stirring occasionally.
Season the sauce with salt and pepper.
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Notes
Don’t rush the mushrooms. Let them cook until browned and tender to develop maximum flavor.
Deglaze well. Scrape up any browned bits when adding the broth and wine—they add depth to the sauce.
Adjust consistency as needed. If the sauce gets too thick, thin it with a splash of broth; if too thin, let it simmer longer.
Season at the end. The broth reduces as it cooks, so wait until the sauce finishes simmering before adding salt.
Serve warm. This sauce thickens as it cools, so reheat gently before serving if needed.