In a large skillet, heat the olive oil and butter over medium heat. Add sliced onions, sugar, and salt and pepper. Stir occasionally for about 15 minutes until golden brown and soft. Add balsamic vinegar and thyme; cook for another 5 minutes.

Preheat your oven to 400°F (200°C). Roll out puff pastry on a floured surface until about ¼ inch thick. Cut into 6 rectangles and transfer to a lined baking sheet. Spread the caramelized onion mixture onto each rectangle.

Crumble goat cheese evenly on top of the caramelized onions. Sprinkle extra thyme for flavor.

Bake the tarts in the oven for 15 minutes, or until puffed and golden brown. If necessary, bake for an additional 3–5 minutes.

Remove from the oven and let cool for about 5 minutes before serving.