Rub pork chops with 2 tablespoons olive oil and sprinkle with 1/2 teaspoon salt and pepper on both sides. Cover and allow to sit at room temperature for 20 minutes.
Oil the grate of a grill and set to medium heat. Add chops and grill for 20 minutes, flipping halfway through. Internal temperature taken with a meat thermometer should read 145 to 160 degrees.
Toss the asparagus in 1/2 tablespoon olive oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Add alongside the pork chops, after the chops have cooked for 15 minutes.
Thread cherry tomatoes onto skewers and drizzle with 1/2 tablespoon oil and sprinkle with 1/4 teaspoon of salt and pepper.
Grill asparagus and tomatoes for about 5 minutes, until asparagus is slightly tender and tomato skins have blackened a bit in places. After removing pork chops from grill, allow to rest 5 minutes before serving.
Cover veggies until ready to serve. Tomatoes may be served on skewers or removed from skewers.
Serve asparagus and tomatoes alongside pork chops and drizzle with pesto.