1. Preheat the oven to 425°F degrees. 2. Line a sheet pan with parchment paper. 3. Heat 3 tablespoons of olive oil in a large skillet over medium-low heat and add the onions and garlic; sauté for 15 to 20 minutes, stirring frequently, until the onions are limp and there is almost no moisture remaining in the skillet. 4. Add 1/2 teaspoon salt, 1/4 teaspoon pepper, the wine and thyme and continue to cook for another 10 minutes, until the onions are lightly golden. 5. Unfold each sheet of puff pastry on a lightly floured surface and roll it lightly to an 11-by-11-inch square. 6. Using a six-inch-wide saucer or other circular object as a guide, cut 2 (six-inch) circles from each sheet of puff pastry, discarding the scraps. 7. Repeat with the second sheet of pastry. 8. Using the tip of a sharp paring knife, score a circle 1/2 inch inside the edge of each pastry. Prick the pastries all over with the tines of a fork and place them on the sheet pan. 9. Sprinkle a tablespoon of the grated Parmesan on each round, staying inside the scored border. 10. Place 1/4 of the onion mixture on each circle, again staying within the scored edges. 11. Crumble 1 ounce of goat cheese on top of the onions. 12. Place a slice of tomato in the center of each tart. 13. Brush the tomato lightly with olive oil and sprinkle with basil, salt, and pepper. 14. Finally, scatter 4 or 5 shards of Parmesan on each tart. 15. If the pastry is warm, chill for 15 minutes. 16. Bake for 20 to 25 minutes, until the pastry is golden brown. 17. Garnish each with a sprig of thyme and a drizzle of olive oil. 18. Serve warm. 19. Enjoy! ---------------------------------------------------------------------------
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