Preheat the oven to 200°C (400°F) and line a baking tray with parchment paper.

In a skillet, heat olive oil and butter over medium heat. Add the sliced onions, sugar, and salt. Cook, stirring occasionally, for 15-20 minutes until the onions are golden and caramelized. Remove from heat and let cool slightly.

Roll out the puff pastry and cut it into small circles or squares using a cookie cutter or knife. Place the pastry pieces on the prepared baking tray.

Spoon a small amount of caramelized onions onto each pastry piece and top with grated cheese. Sprinkle with black pepper and fresh thyme or rosemary if desired.

Bake for 12-15 minutes, or until the pastry is golden and the cheese is melted and bubbly.

Let cool slightly before serving.