Preheat the oven to 400°F.
On a Silpat or piece of parchment paper, roll the pastry sheet into a 10 by 14-inch rectangle. Use a sharp knife to score a 3/4-inch-wide border around the pastry rectangle. Prick the dough with a fork inside the score line and refrigerate until ready to use.
Heat 1 tablespoon of olive oil in a medium skillet. Add the garlic and breadcrumbs and stir occasionally over moderate heat until the crumbs are golden brown and toasted. Let cool at room temperature.
To assemble the tart, sprinkle the breadcrumbs over the pastry dough inside the score line and dot them with teaspoons of pesto. Lay the tomatoes on top. Follow with the Taleggio cheese slices. Sprinkle liberally with sea salt.
Bake for 25-35 minutes, until the edges of the tart are golden and the cheese is bubbly. Sprinkle with the fresh thyme leaves and lightly drizzle with olive oil. Serve hot or warm.