In a large skillet, heat 2 tablespoons of olive oil and 1 tablespoon of butter over medium heat until shimmering. Add 3 sliced yellow onions along with 1 tablespoon of sugar, and season with salt and pepper. Fry gently for 15-20 minutes until golden brown and jammy. Stir in 1 tablespoon of balsamic vinegar and thyme, cooking for an additional 5 minutes.

While the onions are caramelizing, lightly flour a clean surface and roll out one sheet of puff pastry to about ¼ inch thick. Cut the pastry into 6 equal rectangles and transfer to a parchment-lined baking sheet.

Once the onion mixture has cooled slightly, spread a generous layer of caramelized onions over each pastry rectangle, leaving a ½ inch border. Crumble 4 ounces of goat cheese on top of the onions.

Preheat your oven to 400°F (200°C). Bake the tarts for about 15 minutes, or until puffed up and golden brown. Allow them to cool slightly before serving.