Whisk together the oil, balsamic vinegar, parsley, rosemary, cumin, garlic and 2 tablespoons mint in a medium bowl. Place the lamb into a resealable plastic bag and pour half of the marinade over the lamb. Season with salt and pepper, seal the bag and refrigerate for 1 to 2 hours.
Add the lemon zest and juice and remaining 6 tablespoons mint to the remaining marinade and whisk to combine. Season with salt and pepper and set aside.
Heat a large grill pan over medium-high heat until very hot; lightly brush with oil.
Remove the lamb from the bag, letting the excess marinade drip off (discard the marinade). Season with salt and pepper. Grill the chops, turning once, about 3 minutes per side for medium-rare.