On a lightly floured surface, unfold puff pastry and dust with flour on top. Use a rolling pin to gently roll pastry so it is a bit thinner.
Line a 9 x 13 sheet pan with parchment paper and place puff pastry onto pan. If there is excess dough hanging, cut it off so the pastry sits in the pan nicely.
Use a knife to score a half inch border around the pastry and use a fork to dock holes all over the middle of the pastry. This will help prevent puffing up. Pre bake the puff pastry for 10 minutes until lightly golden brown. Once done, remove from oven and let cool for 15 minutes. The pastry will have puffed but will deflate as it settles.
Meanwhile, place the sliced tomatoes on a paper towel lined plate and sprinkle with salt. Let tomatoes sit for at least 15-20 minutes. Then press the tomatoes with more paper towels to soak up excess moisture.
Layer the sliced tomatoes, peaches and mozzarella onto the puff pastry. Drizzle with olive oil and sprinkle everything with salt and bake for 25-28 minutes, until the pastry is lightly golden brown and cheese has melted.
While the tart bakes, make the basil oil by blending the olive oil and basil leaves together. Once the tart is finished baking, remove it from oven and let cool for 5 minutes.
Garnish the caprese tart with dollops of basil oil, drizzle of aged balsamic and fresh basil leaves.
Notes
Use any variety of tomatoes, just be sure to drain and press with paper towels to remove excess moisture.
Use low moisture mozzarella to prevent excess moisture.
If the crust is browning too quickly, cover with foil for the last few minutes.