In a large saucepan melt 1/4 cup of the butter and cook the carrots, onion, and garlic over low heat until softened, about 5 minutes. Stir in the tomato purÄe, the bouquet garni, juniper berries, cloves, and nutmeg and bring to a boil. Reduce heat and simmer for 2 hours. PurÄe the sauce in a blender or food processor, then strain it into a medium saucepan and boil vigorously until it reduces to 1 1/2 cups. Season with salt and pepper. Heat a large pan over a moderate heat and add the duck breasts skin side down and cook until the skin is browned and crisped, 2 to 3 minutes. Turn the breasts and continue cooking until medium-rare, about 6 minutes longer. Re-heat the sauce and whisk in the remaining butter, a little at a time, warming the sauce through without boiling it. To serve, slice each duck breast into several pieces on the diagonal and spoon over the sauce.
