Tomatoes are the essence of summertime. For this recipe, you need tomatoes that are at the peak of ripeness. Everything comes together very fast in this dish, which makes a decorative appetizer or main course.
Preheat the oven to 375 degrees F. Line a shallow rimmed baking sheet with parchment paper.Unfold the puff pastry onto a lightly floured surface into a 1/4-inch thick rectangle the shape of the baking sheet.Slice the tomatoes and sprinkle them with the optional sugar and a pinch of salt. Slice the cherry tomatoes in half.Gently roll the puff pastry over a rolling pin and unfold onto the lined baking sheet. Trim any excess with a paring knife. Using the tip of the knife, lightly score a border about 1/2 inch from the edge of the pastry. Prick the dough inside the border all over with the tines of a fork to prevent it from puffing up too much during baking. Chill slightly, if you have a few extra minutes.
Arrange the tomatoes on the pastry in a single layer (crowding or overlapping the tomatoes will make the puff pastry soggy). Strip the branches of thyme, scattering the leaves over the tomatoes. Drizzle the tart with some olive oil and season with freshly ground black pepper.
Bake the tart until the pastry is crisp and deeply browned on the bottom and around the edges, about 40 minutes. Remove from the oven. Drizzle with best-quality olive oil and sprinkle liberally with finishing sea salt. Cut into portions and serve to your guests.