Preheat the oven to 400 degrees farenheit.
Slash the edges of the chops in 2 or 3 places to prevent curling. Sprinkle generously with salt and pepper.
Coat the bottom of a large, ovenproof frying pan with the olive oil and heat over medium-high heat. When the oil starts to smoke, add the lamb chops and sear them to a golden brown on both sides, about 2 minutes on each side. (Do not crowd the pan; use 2 frying pans if necessary).
Transfer the pan(s) to the oven and roast until an instant-read thermometer inserted away from the bone registers 130-135 degrees Farenheit or the chops are a deep pink when cut into near the bone for medium rare, 6-8 minutes.
Transfer to a platter and let rest, tented loosely with aluminum foil, while you make the sauce.
To make the sauce, drain off all but 1 Tb of drippings from the pan. Add the shallots and garlic and saute, stirring often, until softened, 3-4 minutes. Add the Port and stock and bring to a boil over high heat. Cook until reduced by half, about 5 minutes.
Reduce heat to medium. Whisk in the mustard and then the butter pieces. When the butter has melted and combined and the sauce is smooth, season to taste with salt and pepper.
Transfer the chops to individual plates, spoon sauce on top, and serve.