Over high heat, heat 2 tablespoons evoo in each of two large saute pans. Place chops in one layer in each pan. If all the chops will not fit at one time, brown them in two batches. Cook chops until brown, about 3 minutes on each side. When chops are cooked to your desired doneness, remove from pan and place on a baking sheet. Cover tightly with foil. Place in oven and turn oven off. Chops will stay warm in the retained heat without overcooking.
Reserving 2 tablespoons fat, drain fat from the pans. Return the reserved fat to one saute pan, over medium heat. Add shallots and cook, stirring, for 1 minute. Add red wine and broth and cook until sauce is reduced by half, about 4 minutes.