In a bowl, combine minced garlic, lemon zest, lemon juice, olive oil, ground cumin, salt, and pepper. Rub this marinade all over the lamb chops. Cover and refrigerate for at least 1 hour, or overnight for a deeper flavor.
Heat a heavy skillet (preferably cast iron) over medium-high heat. Once the pan is very hot, add a splash of olive oil.
Place the lamb chops in the skillet and sear for about 3-4 minutes on each side, or until a nice golden crust forms. If your chops are thicker or you prefer them more done, you can reduce the heat to medium and cook for an extra 2 minutes per side, or finish them in a preheated oven at 180°C (350°F) for 5-7 minutes. Remove the chops from the skillet and let them rest for 5 minutes.
In a small bowl, whisk together the Greek yogurt, chopped mint, minced garlic, lemon juice, salt, and pepper. Drizzle in the olive oil if using. Mix until well combined.
Plate the lamb chops and either drizzle the mint yogurt sauce over them or serve it on the side. Garnish with extra mint if desired, and enjoy with your favorite sides.