Bring a medium pot of salted water to a boil, add carrots and cook until just tender, 3 to 4 minutes. Drain, rinse in cold water and drain again; set aside. Meanwhile, season lamb chops all over with salt and pepper. Heat oil in a large skillet over medium-high heat, arrange four of the lamb chops in skillet and cook, flipping once, until deep golden brown and cooked to desired doneness, about 5 minutes; transfer to a large plate, tent with foil and set aside. Repeat process with remaining lamb chops.

Add shallots and thyme to skillet and cook until just softened, 2 to 3 minutes. Carefully add broth and cook, scraping up any browned bits, until reduced by three-quarters, about 5 minutes. Add wine and simmer vigorously until reduced by half, about 5 minutes more. Add peas, onions, carrots, butter and sugar and cook, tossing often, until tender and glazed, 3 to 4 minutes; discard thyme. Remove skillet from heat, add spinach and toss gently to wilt. Spoon vegetables and sauce onto four large plates, top with lamb chops and serve.