Cook the flour in the melted butter in a frying pan, whisking often, until a golden blonde color. Set aside.
Reduce red wine by half in a 1-quart pot over medium heat, then set aside.
Melt remaining tablespoon butter in a small saute pan over medium heat, then add chopped mushrooms, garlic, onions, peppers and a pinch of salt and black pepper. Cook, stirring, until vegetables are soft, 2 to 3 minutes. Let vegetables cool for a couple of minutes, then add them to a food processor and liquify as much as possible, adding 1/4 cup beef broth if the vegetables become too sticky. Transfer back to the pan and add the reduced wine, then add the remaining 2 3/4 cups beef broth and bring back to a rolling boil. Reduce the heat and thicken with the roux until the sauce is as thick as you would like it to be. Add the sliced mushrooms, salt and black pepper to taste, then simmer for 2 additional minutes.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.