Season the racks with oil and some of the rosemary. In a hot pan, place the rack in, fat side down, and roast at 400°F for four minutes. Turn lamb and roast an additional three minutes. Remove from oven and let rest, preferably on a rack, until ready to cut. Reserve drippings from the meat.
Place the fingerling potatoes and bay leaf in a pot of salted water; bring to a boil and cook for four minutes. Turn the heat off and let the potatoes cool in the liquid. Meanwhile, peel the asparagus.
Place the asparagus and potatoes in a baking dish and season with the olive oil, butter, lemon juice, salt and pepper. Roast the vegetables in at 400° F for eight minutes. Remove the vegetables and keep warm until serving.
Whisk all ingredients together in a non-reactive bowl until well incorporated. Refrigerate until needed.
Add all ingredients, except the oil, to a blender and mix on high for two minutes. Turn down and slowly drizzle in the oil. Season to taste with salt and pepper.
Cut each rack in half and in half again, creating double bone chops. Serve two double bone chops on each plate. Place the asparagus and potatoes next to the lamb, and top a dollop of horseradish crème fraiche. Spoon pan juices over the lamb and drizzle mint sauce in front of it.