Unfold a defrosted sheet of puff pastry on a lightly floured surface and roll it lightly to an 11 x 11 inch square. Using a 6 -inch-wide saucer or bowl as your guide, cut 2 circles from the sheet of pastry. Repeat this process with the second sheet of puff pastry. You should have 4 circles in all. Discard the scraps pastry or use in another recipe.

Place the 6 inch pastry cut-outs onto 2 cookie sheets lined with parchment paper. Refrigerate until ready to use.

Preheat the oven to 425 degrees.

Heat 3 tablespoons of olive oil in a large skillet over medium to 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. Add 1/2 teaspoon of salt, 1/4 teaspoon pepper, the wine, and the thyme. Continue to cook for another 10 minutes, until the onions are lightly browned. Remove from the heat.

Using a sharp paring knife, score a 1/4-inch-wide-border around each pastry circle. Prick the pastry inside the score lines with a fork and sprinkle a tablespoon of grated parmesan on each round, staying inside the scored border.

Place one-quarter of the onion mixture on each circle, again staying within the scored edge. Crumble 1 ounce of goat cheese on top of the onions. Place a slice of tomato in the center of each tart. Brush the tomato lightly with olive oil and sprinkle with basil, salt, and pepper. Finally, scatter 4 or 5 shards of parmesan on each tart.

Bake for 20 to 25 minutes, until the pastry is golden brown. The bottom sheet pan may need an extra few minutes in the oven. Serve hot or warm.