1. Preheat oven to 375°F. Roll out puff pastry on a sheet of lightly floured parchment paper into an 11x9 inch rectangle, smoothing out creases. Prick pastry in a few places with a fork, leaving a 1 inch border around the edges, then slide parchment paper onto a rimmed baking sheet.
2. Combine pesto and 1 tbsp. oil in a small bowl and brush dough with oil, staying within the border.
3. Arrange tomatoes on top. Sprinkle with salt & a few grinds of pepper. Sprinkle with parmesan cheese and drizzle with 1 tbsp. oil.
4. Bake tart until edges of pastry are browned, puffed, and crisp, 30-35 minutes. Let tart cool 10 minutes before cutting. Drizzle with more oil and top each with a dollop of ricotta cheese, fresh basil and balsamic glaze/vinegar.