Preheat the oven to 425F and line a large baking pan with parchment paper
Unfold the puff pastry onto the prepared baking sheet, gently smoothing out any fold marks
Spread the pesto over the puff pastry leaving about a half-inch around the edge as a crust
Sprinkle the shredded cheese on top of the pesto covered pastry
Bake the pastry for 15-18 minutes until the pastry is puffed and the cheese is golden in color
Remove from oven and allow the pastry to cool for 10-15 minutes
Layer the sliced tomatoes on top of the pastry
Finish with a drizzle of olive oil, fresh basil, and a heavy pinch of coarse sea salt and black pepper