Preheat your oven to 400°F (200°C). If your chicken breasts are thicker than 1 inch, place them between plastic wrap and gently pound to even thickness. Pat the chicken completely dry with paper towels and season both sides generously with salt and pepper.

Heat olive oil in a large skillet over medium-high heat until the oil moves freely across the pan and looks glossy. Add the chicken and cook for 6-7 minutes per side without moving, until golden brown and the internal temperature reaches 165°F (75°C).

Remove the chicken from the skillet and let it rest on a cutting board for 5 minutes before slicing into thin strips.

Lay out the flatbreads on a baking sheet. Spread about 1/4 cup of basil pesto over each piece, going right to the edges but keeping the layer relatively thin.

Distribute the sliced chicken evenly over the pesto-covered flatbreads. Sprinkle shredded mozzarella cheese over the chicken, followed by halved cherry tomatoes, then top with grated Parmesan cheese.

Bake in the preheated oven for 10-12 minutes until the cheese is melted and forming small bubbles, and the edges are golden brown. Optionally, switch to broil for the last 1-2 minutes for a crispy top, watching closely to prevent burning.

Remove from the oven and let cool for a minute. Slice into quarters or halves and garnish with fresh basil leaves if desired. Serve warm.