If you like mushrooms, use a mix of varieties—portobello, hen-of-the-woods and oyster would all be delicious. Slideshow: More Beef Recipes
Preheat the oven to 350°. In a large enameled cast-iron casserole, heat 2 tablespoons of the oil. Place the flour in a shallow bowl. Season the beef with salt and pepper and dredge in the flour, shaking off the excess. Add half of the beef to the casserole and cook over moderately high heat, turning, until browned, about 5 minutes; transfer to a plate. Repeat with the remaining beef and 2 tablespoons of oil.
Add the shallots to the casserole and cook over moderate heat, stirring occasionally, until lightly golden, 2 to 3 minutes. Stir in the tomato paste and garlic and cook, stirring, until deep red, about 2 minutes. Return the beef and accumulated juices to the casserole. Add the wine and cook until reduced by half, about 5 minutes. Add the stock, thyme and bay leaves and bring to a boil.
Cover the casserole and transfer to the oven for about 1 hour, cooking until the beef is almost tender. Stir in the carrots and mushrooms, cover and cook for 30 minutes, until the beef and vegetables are tender. Discard the thyme and bay leaves and garnish with parsley. Serve hot with crusty bread.
The beef burgundy can be refrigerated for 3 days and reheated before serving.
I have made this on several occasions and it always turns out great.