Season the lamb chops all over with 1-1/2 tsp. salt and 1/2 tsp. pepper. Heat the oil in a large skillet over medium-high heat. Put 2 of the chops in the skillet and cook, flipping once, until deep golden-brown and medium rare (130°F), about 10 minutes. Transfer to a large plate, cover loosely with foil, and keep warm. Repeat with the remaining 2 chops.
Add the shallots to the skillet and cook, stirring, until softened, about 1 minute. Add the broth and wine and cook, scraping up any browned bits, until reduced by half, 4 to 5 minutes. Reduce the heat to medium low, stir in the mustard and lemon juice, and cook for 1 minute more. Add the butter a piece or two at a time, swirling the skillet to melt it into the sauce. Remove the skillet from the heat and stir in the dill. Season to taste with salt and pepper. Serve the lamb with the sauce.
The lamb and sauce pack a lot of flavor; keep the side simple with Basic Roasted Green Beans.
nutrition information (per serving):
Photo: Scott Phillips