Preheat oven to 400 degrees F. Line a baking sheet with aluminum foil and set aside.
Season both sides of the rack of lamb with salt and pepper.
Heat 2 tbsp oil in a large skillet over high heat. Place lamb in the hot skillet, fatty side down first, browning each side for 3-4 minutes. Transfer lamb to the foil-lined baking sheet.
In a small bowl, stir together pistachios, parmesan cheese, rosemary, and 1 tbsp olive oil. Spread the mustard on the fat-side of the lamb. Using your hands, pat the pistachio mixture on top of mustard and press down so that it sticks.
Bake for 20-25 minutes, until the crust is golden and lamb is pink in the center, or to the doneness of your liking. Transfer to a plate and let rest 10 minutes before carefully slicing in between the bones into individual chops.