Preheat the oven to 400 degrees Fahrenheit. Toss the cherry tomatoes with 1 tablespoon of olive oil and a pinch of salt and pepper.
Spread the tomatoes evenly on a baking sheet and roast for 15 to 20 minutes until they are blistered and tender. Set aside.
In a food processor, combine the fresh mint leaves, rosemary, garlic, pine nuts, and Parmesan cheese. Pulse until the ingredients are coarsely chopped.
With the food processor running, slowly drizzle in the 1/2 cup of olive oil until the pesto reaches a smooth, cohesive consistency. Taste and season with salt and pepper.
Pat the lamb chops dry with paper towels. Season both sides generously with the remaining salt and black pepper.
Heat a large cast-iron skillet or heavy-bottomed pan over medium-high heat with the remaining 1 tablespoon of olive oil. Once the oil is shimmering, add the lamb chops.
Sear the lamb chops for 3 to 4 minutes per side for a medium-rare internal temperature of 135 degrees Fahrenheit.
Transfer the lamb chops to a plate and let them rest for 5 minutes.
Serve the rested lamb chops alongside the roasted cherry tomatoes, generously spooning the fresh mint pesto over the meat.