Brown beef cubes on all sides in 1/4 cup hot butter or margarine in large skillet, or slow-cooker if it has a browning unit. Pour beef and drippings into slow-cooker. Add carrots, chopped onions, chopped garlic, beef broth, wine, tomato paste, fines herbes, salt and pepper, mushrooms, and white onions. Cover pot and set at Low. Cook for 10 hours.
Remove lid and skim excess fat from surface. Turn heat setting to High. Cover and let bubble. In a bowl, mix flour and 1/4 cup butter until creamy. Add to stew and sir until it is well blended and the stew thickens. Season to taste with salt and pepper. Serve hot with boiled potatoes.
YIELD: Serves 8.