Preheat an oven to 400°F. Line a rimmed baking sheet with parchment paper.
Unfold the pastry sheet on a lightly floured work surface. Roll out into a 9-by-13-inch rectangle about 1/8 inch thick. Transfer the rectangle to the prepared baking sheet. Using a fork, prick the rectangle evenly all over. To create a border on the tart, trace a 1/2 inch border on the outside of the puff pastry, slicing halfway through the puff pastry. Be careful not to cut through the entire puff pastry.
Arrange the cherry tomato halves, sliced tomatoes, pancetta and cheese evenly on top of the pastry rectangle. Sprinkle evenly with salt and pepper, and top with the thyme sprigs.
Bake until the pastry is puffed and golden brown, about 20 minutes. Remove from the oven and transfer to a work surface. Cut the tart into pieces and serve with a bowl of basil vinaigrette for drizzling. Add tiny basil leaves on top to garnish.