Step 1Rub a cut clove of garlic over the surface of the lamb chops. Drizzle them with 1 tablespoon of the olive oil and rub it over the surface of the lamb. Sprinkle the lamb with the herbes de Provence and salt to taste and rub it into the lamb. Cover and let the lamb stand while you prepare the remaining ingredients
Step 2Whisk together the mustard, sugar and balsamic vinegar. Gradually drizzle in the remaining 2/3 cup of olive oil, whisking to form an emulsion. Stir in the shallot, 2 tablespoons of the mint, the chives and salt and pepper to taste.
Step 3Toss together the butter lettuce, arugula, sorrel and watercress in a large bowl. Add the olives, fava beans and remaining 1/4 cup of mint and toss to mix. Cover the greens and refrigerate until ready to serve.
Step 4Meanwhile, heat the grill over medium-high heat or heat the broiler. Grill or broil the lamb chops until crispy brown on the outside and medium rare on the inside, three minutes a side or to 145 degrees on a meat thermometer.
Step 5Add enough dressing to moisten the greens and toss until the greens are evenly coated. Divide the greens onto plates and top each plate with a lamb chop.