Trim any excess fat from the lamb and season lightly on both sides with salt and pepper.
Melt half the butter with the oil in a shallow, flameproof casserole and fry off the lamb in batches until browned. Drain to a plate.
Return the lamb chops to the casserole, arranging them side by side, and sprinkle with the rosemary and garlic. Tuck the onions and mushrooms around them, then place the potatoes on top. Pour the stock over.
Cover with a lid or foil and bake in a preheated oven, 160°C (325°F), Gas Mark 3, for 1½ hours. Dot with the remaining butter, return to the oven and cook, uncovered, for a further 45 minutes or until the potato topping is crisped and browned.