Melt butter with oil in skillet over high heat. Sprinkle chicken with salt and pepper. Cook, skin side down, until brown. about 5 minutes. Turn over; cook 1 minute or so. Using tongs, transfer chicken to plate
Add shallots to same skillet; reduce heat to medium low. Saute until soft about 3 minutes. Add Brandy; simmer until liquid is reduced, scrapping up browned bits, about 2 more minutes. Whisk in broth. Return chicken to skillet. skin side up. Reduce heat to med-low. Cover and simmer until chicken is cooked, about 25-30 minutes.
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 and enjoy your wonderful meal. xooxxoxo