Combine paprika, dried thyme, kosher salt, black pepper, and brown sugar in a small bowl to make the dry rub.

Place lamb chops in a baking dish and evenly sprinkle half the dry rub over one side, then flip and sprinkle the remaining rub on the other side. Pat to adhere.

Drizzle 2 tablespoons olive oil and minced garlic over the lamb chops and toss to coat thoroughly.

Cover the baking dish with plastic wrap and refrigerate for at least 4 hours, preferably overnight, to marinate.

Remove lamb chops from fridge and let reach room temperature before cooking.

In a bowl, whisk together Greek yogurt, mayonnaise, salt, cayenne pepper, honey, and lemon juice to prepare the aioli.

Heat a large cast iron skillet over high heat and add 1 tablespoon olive oil.

When oil is hot and shimmering, add half the lamb chops and cook 2-3 minutes per side until browned and medium-rare (130ºF internal temperature). Adjust cooking time for desired doneness.

Transfer cooked lamb chops to a plate and let rest while cooking the remaining chops with another tablespoon of olive oil in the skillet.

Spread the aioli evenly on a serving platter, place rested lamb chops on top, garnish with chopped mint if desired, and serve.