Begin by thinly chopping the garlic, rosemary, thyme, and mint. Combine and add the hot pepper, salt and black pepper and mix together.
Place the rack of lamb, fat side up, on a cutting board and spread the mustard all along the top of the meat. Sprinkle more than half of the herb mix on top and pat into the mustard. Flip the rack of lamb over and sprinkle the rest of the herb mix on the rest of the meat. Place on a dish and cover with saran wrap and let it marinate in the refrigerator for a couple of hours.
Once marinated, set your oven to 400°F. Place the rack of lamb in a baking pan and drizzle olive oil around and over the rack of lamb.
Begin preparing your potatoes. Place the potatoes in a bowl and add the garlic, olive oil, rosemary, thyme, salt, black pepper, and hot pepper flakes. Toss to mix together and the add them into the baking pan next to the rack of lamb.
Place the baking pan on the third rack from the bottom of the oven and cook for thirty-five to forty minutes. After forty minutes, remove the baking pan from the oven and place the rack of lamb onto a dish. Cover the rack of lamb with aluminium foil to let sit. Place the baking pan back in the oven for ten more minutes to let the potatoes finish cooking.
Once the potatoes are done cooking, remove from the oven. Cut each of the lamb ribs and serve with the potatoes. Enjoy and cin cin!