Unfold a sheet of puff pastry on a lightly floured surface and roll it lightly. Using a 2 ¾ inch biscuit cutter, cut as many rounds as you can from your pastry sheet.

Place the rounds on a parchment-lined baking sheet. Score the rounds with a slightly smaller biscuit cutter (I used a 2 ½-inch cutter) without cutting all the way through.

Refrigerate the pastry while preparing the rest of the ingredients.

Preheat the oven to 425º.

Heat about a generous tablespoon of olive oil in a skillet over medium to low heat and add the onions and garlic. Saute for 15 to 20 minutes, stirring frequently, until the onions are soft and the liquid has evaporated.

Add ¼ teaspoon salt, freshly ground black pepper, the wine, and thyme, and continue to cook for another 10 minutes, until the onions are lightly browned. Remove from the heat.

Using a sharp paring knife, score a ¼-inch-wide border around each pastry circle. Prick the pastry inside the score lines with the tines of a fork and sprinkle some grated Parmesan on each round, staying inside the scored border.

Divide the onion mixture among your tartlets, again staying within the scored edge. Crumble 1-1 ½ teaspoons Boursin 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.

Bake for 20 to 25 minutes, until the pastry is golden brown. Serve hot or warm.