Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Season the chicken breasts with salt and pepper.
Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Cook the chicken for 5-7 minutes on each side until golden brown and cooked through (165°F internal temperature). Allow to rest before shredding.
Spread basil pesto evenly over flatbreads on the baking sheet. Top with shredded chicken, mozzarella, and Parmesan cheese.
Add halved cherry tomatoes on top, then bake for 10-15 minutes until bubbly and golden.
Let cool slightly before garnishing with fresh basil leaves and slicing into pieces.