Heat olive oil in a skillet over medium heat. Add sliced onions and cook, stirring occasionally, for about 20 minutes until they are caramelized and golden brown. Season with salt, pepper, and balsamic vinegar if using.

Preheat the oven to 400°F (200°C). Roll out the puff pastry on a floured surface and cut into 4 squares. Place the squares on a baking sheet lined with parchment paper. Brush the edges with beaten egg. Spoon the caramelized onions onto the center of each square and sprinkle with crumbled goat cheese and fresh thyme.

Bake in the preheated oven for 15-20 minutes, or until the pastry is golden and puffed. Remove from the oven and let cool slightly before serving.