Preheat your oven to 400°F.

Slice the baby potatoes in half and place them on a baking sheet. Drizzle with olive oil and season generously with kosher salt, black pepper, granulated garlic, and Italian seasoning. Toss well and arrange cut-side down in a single layer. Roast for 25 minutes while you prepare the lamb.

In a small bowl, combine the softened salted butter, minced garlic, minced rosemary, and Dijon mustard. Mix well and set aside.

Pat the rack of lamb completely dry with paper towels and season generously with kosher salt and black pepper on all sides.

Heat the vegetable oil in a large cast iron skillet over medium-high heat. Once hot, place the rack of lamb fat-side down and sear for 4 minutes. Flip and cook for another 2 minutes. Using tongs, carefully sear all remaining sides and edges for a few seconds each until nicely browned.

Remove the skillet from the heat and brush the garlic rosemary butter mixture all over the lamb. The butter will melt immediately when it touches the hot meat, and that's completely fine! Spread the garlic and rosemary evenly over the lamb.

Transfer the cast iron skillet to the 400°F oven and roast for approximately 10 minutes for medium-rare, or until the lamb reaches your preferred temperature. For medium-rare, aim for a final temperature of 130–135°F after resting.

Remove the lamb from the oven, transfer it to a cutting board, and let it rest for 6–7 minutes before slicing between the bones.

Continue roasting the potatoes until they've cooked for approximately 35 minutes total, or until golden brown, crispy, and fork-tender. Sprinkle with freshly grated Parmesan cheese if desired.

Slice the lamb into individual chops and serve immediately with the roasted baby potatoes. Enjoy!