Preheat oven to 325°F.
In a food processor, combine the toasted pistachios, arugula, mint, garlic, olive oil, lime juice, salt, and pepper. Pulse until the mixture is smooth. Adjust salt and pepper to taste.
Pat the American Lamb shoulder dry with paper towels. Season it generously with salt and pepper.
Spread the pistachio-herb mixture generously and evenly over the lamb. Reserve some mixture for drizzling during serving.
Roast for about 2 to 2.5 hours or until the internal temperature reaches your desired doneness (145°F for medium-rare).
Cover the lamb with aluminum foil if it is starting to get too dark.
Remove the lamb from the oven and let it rest for 15-20 minutes before carving.
Slice the lamb shoulder, drizzle over the mint-pistachio sauce, and some pomegranate kernels.
