For the salsa verde: In a medium bowl, add the parsley, olive oil, mint, pistachios, capers, lemon juice and salt and stir with a rubber spatula until combined. Set aside to let the flavors marry.
For the lamb: Meanwhile, heat a grill pan over medium-high heat. Dry the lamb chops well with a paper towel and season with the salt. Brush the grill with olive oil and grill the chops for 4 minutes on each side for medium rare. Remove to a plate to rest for 10 minutes.
Drizzle the chops with some of the sauce and serve the remaining sauce alongside.