Preheat the oven to 160°C (325°F). Wash and thoroughly dry the mutton. With a sharp knife, make several incisions in the meat and insert a slice of garlic into each one.
Generously sprinkle the meat on all sides with salt, black pepper, and marjoram. If using rosemary, place the sprigs under the meat in the baking dish.
Heat the butter or oil in a pan and quickly sear the meat on all sides to brown it. Transfer the seared meat to a baking dish. Scatter the sliced onions and carrots around the meat.
Pour the water or broth over the meat, cover the dish, and place it in the preheated oven. Roast for 2 to 2.5 hours. Baste the meat with the pan juices every half hour.
For a crispy crust, remove the lid for the last 20 minutes of roasting. The meat is done when it is fork-tender and pink inside (medium-rare).