Preheat the oven to 200 degrees Fahrenheit.
Prepare your lamb rub by mixing the dijon mustard, garlic, rosemary, and olive oil together in a dish.
Pat the lamb breast dry with a paper towel.
Season the lamb with salt and pepper on both sides.
Brush the lamb all over with the mustard, rosemary, and garlic mixture.
Place lamb fat side up in a roasting pan or on a baking dish and cook lamb breast for 4 hours.
Turn the temperature of the oven up to 350 degrees Fahrenheit for about 20 to 30 minutes to provide a light crisp to the exterior of the lamb. Keep an eye on your lamb at this point. Some ovens are faster than others to heat. If you notice the exterior getting a bit dark, remove the lamb breast from the oven.
Use an instant-read thermometer to ensure the lamb has reached at least 145 degrees Fahrenheit. You are looking for the fat to render (it will pool at the bottom of the roasting pan), a browned exterior, and a somewhat crisped surface. Let rest for about 10-15 minutes, cut the ribs apart, then serve.