Season lamb with salt and pepper. In a large skillet, melt butter and oil over medium-high heat. When skillet and oil are hot, place chops down in a single layer. Cook for 3 minutes per side or according to desired doneness.
Transfer chops to a plate and loosely tent with foil to retain heat. Spoon out any fat in excess of 1 tablespoon. Add shallots and saute until softened. Stir in mustard and deglaze with cognac, scraping bottom of pan with a wooden spoon to release any browned bits. When cognac has reduced to about 1 tablespoon, stir in cream. Season to taste with salt and pepper. Stir in tarragon leaves immediately before serving. Place two or three chops on each plate and spoon the sauce over them.