Preparation Melt butter with oil in heavy large skillet over high heat. Sprinkle chicken with salt and pepper. Cook, skin side down, until brown, about 5 minutes. Turn over; cook 1 minute. Using tongs, transfer chicken to plate. Add shallots to same skillet; reduce heat to medium-low. Sauté until soft, about 3 minutes. Add brandy; simmer until liquid is reduced, scraping up browned bits, about 2 minutes. Whisk in broth. Return chicken to skillet, skin side up. Reduce heat to medium-low. Cover and simmer until chicken is cooked, about 20 minutes. Transfer to platter; reserve skillet. Whisk cream, tarragon, and mustard into same skillet. Increase heat to high; boil until sauce is thickened, about 2 minutes. Season with salt and pepper. Pour sauce over chicken.
Preparation Melt butter with oil in heavy large skillet over high heat. Sprinkle chicken with salt and pepper. Cook, skin side down, until brown, about 5 minutes. Turn over; cook 1 minute. Using tongs, transfer chicken to plate. Add shallots to same skillet; reduce heat to medium-low. Sauté until soft, about 3 minutes. Add brandy; simmer until liquid is reduced, scraping up browned bits, about 2 minutes. Whisk in broth. Return chicken to skillet, skin side up. Reduce heat to medium-low. Cover and simmer until chicken is cooked, about 20 minutes. Transfer to platter; reserve skillet. Whisk cream, tarragon, and mustard into same skillet. Increase heat to high; boil until sauce is thickened, about 2 minutes. Season with salt and pepper. Pour sauce over chicken.