Step 1Simmer the wine and shallots in a 2 1/2-quart saucepan until reduced by half. Set them aside.
Step 2Meanwhile, melt 2 tablespoons of butter with the oil in a large skillet over medium heat. Add the mushrooms and cook, stirring constantly, until lightly browned, about 3 minutes. Add the onions and cook until lightly browned, about 3 minutes longer. Turn the heat to medium-high and add the broth, garlic, thyme and bay leaf. Simmer until the broth is reduced to 1 cup, about 5 minutes. Add the wine mixture and carrots. Adjust the heat to medium and simmer until the carrots are tender, about 6 minutes.
Step 3In a small bowl, mix together the flour and the remaining tablespoon of butter until thoroughly blended. Add the beef and parsley to the pan. Stir in the butter-flour mixture and cook, stirring, until it's completely absorbed and the sauce is thickened. Add pepper to taste.
Step 4Remove the garlic and the bay leaf before serving. Serve the beef with buttered egg noodles or steamed new potatoes.