Sprinkle beef with salt and pepper. Heat 1 tablespoon butter in saucepan and add shallots and garlic. Cook briefly, stirring and add sliced mushrooms. Cook, stirring about 3 minutes. Add half the dry red wine and stir. Cook until reduced almost by half. Add beef or veal broth. Bring to boil and add the remaining dry red wine and the Madeira wine. Cook until reduced by half. There should be about 1.25 cups.
Heat remaining 1 tablespoon butter in heavy skillet and add beef. Cook the meat on one side about 2-3 minutes or until browned. Turn and cook other side 2-3 minutes. Transfer meat to warm platter.
Add mushroom sauce to skillet and stir to dissolve the brown particles that may cling to edge of skillet. Swirl 4 tablespoons butter into sauce. Serve on top of tenderloins.