Preheat the oven to 400 °F (200 °C).
Spread 2 tablespoons of butter all over the lamb.
Season lamb rack with salt, pepper, garlic powder, and rosemary. Sear it in a lightly oiled saute pan and place it in the oven. For the best results, do this step 2 days before and keep the meat in the refrigerator. If you don't have that much time, it is okay to do it before cooking.
Bake lamb rack for 20 minutes for medium.
You can keep your lamb rack in the oven a couple of minutes longer if you like it crispy and under 16 minutes if you prefer medium rare.
When you remove the rack from the oven, cover it with foil and let it rest for about 15 minutes.
Note: If you wish to fry a lamb rack in a pan, you should cut it into slices before seasoning. Preheat the pan, add a little splash of olive oil, and throw in the lamb chops. In this case, you don't spread butter over lamb, rather warm it up together with olive oil. Fry each side of the slices for about 4 minutes.