Heat olive oil in a skillet over medium heat. Add sliced onions and a pinch of salt. Cook, stirring occasionally, until onions are caramelized and golden brown, about 20 minutes.

If desired, add balsamic vinegar and cook for an additional 2 minutes.

Preheat the oven to 400°F (200°C). Roll out the puff pastry on a floured surface and cut into squares or circles to fit your baking sheet.

Place the pastry on the baking sheet and score a border around the edges. Spread the caramelized onions evenly over the pastry, leaving the border clear.

Sprinkle crumbled goat cheese and fresh thyme over the onions.

Brush the edges of the pastry with the beaten egg. Bake in the preheated oven for 15-20 minutes or until the pastry is golden and puffed.

Remove from the oven, let cool slightly, and serve warm.