Preheat an oven to 400 degrees F. Line a rimmed baking sheet with parchment paper.
In a sauté pan, cook the pancetta until slightly golden brown and most of the fat is rendered out of it, about 2-4 minutes (it will finish cooking on top of the tart in the oven). Remove the pancetta from the pan and lay it on dry paper towels to drain. Set aside.
Unfold the pastry sheet on a lightly floured work surface. Roll out into a 9 x 13-inch rectangle about 1/8 inch thick. Place the pastry onto the prepared baking sheet. Using a fork, prick the pastry evenly all over. Create a border on the tart by tracing a 1/2 inch border on the outside edge of the puff pastry with the tip of a sharp knife, slicing halfway through the dough (be careful not to cut through the entire layer of puff pastry).
Arrange tomato halves and slices on top of the puff pastry. Sprinkle the feta or goat’s cheese on evenly, season with salt and pepper, and half of the thyme and basil.
Bake until the pastry is puffed and golden brown and the tomatoes are bubbling, about 20 minutes. Add the pancetta on top of the pastry halfway through baking, so as not to overcook.
Meanwhile, combine all the ingredients for the basil vinaigrette in a food processor or blender and puree for 1 minute until very smooth. Set aside
When finished baking the tart, remove from the oven and place onto a work surface. Cut the tart into pieces and place them on a serving platter. Drizzle with the basil vinaigrette, sprinkle with fresh thyme and basil and serve immediately.
*You can refrigerate the vinaigrette for up to 3-4 days.
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