Method

1. Spread 2 tablespoons of the butter over the bottom of each of four heavy small ovenproof sauté pans.

2. Sprinkle 3 tablespoons of the sugar over the butter in each small pan.

3. Cut the onion crosswise into four 1-inch-thick slices, keeping the rings of each slice intact.

4. Place one onion slice atop the sugar and butter in each small pan.

5. Refrigerate while you prepare the pastry.

6. Unfold the puff pastry sheet and roll it out on a lightly floured work surface to a 12-inch square.

7. Cut out four 5-inch rounds from the puff pastry sheet.

8. Drape 1 pastry round atop each onion slice and tuck the edges down to cover the onions.

9. Pierce the tops of the pastry rounds with a sharp knife and refrigerate for 20 minutes.

10. Meanwhile, preheat the oven to 375°F.

11. Simmer the balsamic vinegar in a heavy small saucepan over medium heat for 10 minutes or until it is reduced by half and coats the bottom of the pan when the pan is tilted.

12. Set aside and cool.

13. The balsamic reduction will continue to thicken and become syrupy as it cools.

14. Place the sauté pans with the tarts over medium heat and cook for 5 minutes, or just until the sugar melts and forms a very pale golden caramel sauce around the tart.

15. Don’t allow the sauce to darken at this point, since it will continue to darken in the oven.

16. Transfer the pans to the oven and bake for about 15 minutes or until the pastries puff and are deep golden brown and the sauce darkens.

17. Let the tarts stand 2 minutes or until the sauce stops bubbling. Swirl the tarts gently to help loosen the onions from the bottom of the pans.

18. Invert each tart onto a plate, using a metal spatula if necessary.

19. Immediately place 1 slice of cheese atop each hot tart.

20. Drizzle the balsamic reduction around the tarts and serve.