Preheat the oven to 200C. Season the lamb chops with salt and pepper. Heat 1 tablespoon olive oil in a large ovenproof skillet over high heat. Add the lamb and brown on all sides. Transfer the skillet to the oven and roast to desired doneness, about 15 minutes for medium-rare. Let rest for 5 minutes.
For the mint walnut pesto, combine the walnuts, mint, parsley, feta, garlic, and ½ teaspoon salt in a food processor and pulse until coarsely chopped. With the motor running, slowly add the olive oil and process until emulsified.
Serve the lamb chops drizzled with the pesto.
