Preheat oven to 400°F and line a sheet pan with parchment paper.
Toss the halved potatoes with 1 tablespoon olive oil, salt, and pepper, then arrange on one side of the sheet pan.
Rub chicken thighs with pesto, coating both sides, and place them skin-side up on the other side of the pan.
Roast for 20 minutes until chicken skin begins to crisp and potatoes start to brown.
Toss cherry tomatoes with remaining olive oil and minced garlic, then add them to the pan around the chicken.
Continue roasting for 10 more minutes until chicken reaches 165°F internal temperature and tomatoes have burst.
Garnish with fresh basil and parmesan cheese before serving.