Prepare the turnips: Preheat your oven to 400°F (200°C). Toss cubed turnips with olive oil, salt, garlic, and herbs. Spread on a baking sheet and roast for 25–30 minutes, flipping halfway, until golden and tender.
Season the lamb: Rub the lamb chops with olive oil, garlic, rosemary, salt, and pepper. Let them sit at room temperature while the turnips roast.
Cook the lamb: Heat a cast iron or heavy skillet over medium-high heat. Sear the lamb chops for 3–4 minutes per side for medium-rare (or longer if desired). Let them rest for 5 minutes before serving.
Serve: Plate the lamb chops alongside the roasted turnips. Drizzle with any pan juices and garnish with extra rosemary if desired.