Preheat oven to 400 degrees F. If chicken breasts are thicker than 1 inch, pound to even thickness between plastic wrap. Pat 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 glossy and moving freely. Add chicken and cook for 6 to 7 minutes per side without moving until golden brown and internal temperature reaches 165 degrees F.

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

Lay flatbreads on a baking sheet. Spread about 0.25 cup of basil pesto over each piece in a thin, even layer going right to the edges. Avoid using too much pesto as it can make the flatbread center soggy.

Distribute sliced chicken evenly over the pesto-covered flatbreads. Sprinkle shredded mozzarella over the chicken, scatter halved cherry tomatoes on top, then finish with freshly grated Parmesan.

Bake for 10 to 12 minutes until cheese is melted and forming small bubbles and flatbread edges are golden. For a crispier top, switch to broil for the last 1 to 2 minutes, watching closely to prevent burning.

Remove from oven and cool for 1 minute. Slice each flatbread into halves or quarters, garnish with fresh basil leaves if using, and serve warm.