Preheat oven to 400 degrees F. Prick tomatoes with a fork or the tip of a sharp knife. In an ungreased 15x10x1-inch baking pan, combine tomatoes, onion, oil, rosemary, salt, and pepper. Roast for 25 to 30 minutes or until onion is tender. Remove from oven. Sprinkle with vinegar; cool.
Meanwhile, line a large baking sheet with parchment paper or foil. On a lightly floured surface, unfold puff pastry. Using a 3-inch round cookie cutter, cut pastry into rounds. Place rounds on the prepared baking sheet.
Spoon about 2 tablespoons of the roasted tomato mixture onto each pastry round. Bake for 15 to 20 minutes or until edges are puffed and golden brown. Let stand on baking sheet for 5 minutes before serving. Garnish with cheese. Makes about 18 tartlets.