Tartelettes aux Oignons Caramélisés (Caramelized Onion Tartlets)

Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.

Heat olive oil and butter in a large skillet over medium heat. Add the sliced onions and cook, stirring occasionally, until softened and translucent, about 10 minutes.

Reduce the heat to low, add brown sugar, balsamic vinegar, salt, and pepper. Continue to cook, stirring frequently, until the onions are deeply caramelized and golden brown, about 20-25 minutes. Watch carefully to prevent burning.

Stir in the fresh thyme.

While the onions are caramelizing, roll out the puff pastry on a lightly floured surface to about 1/8 inch thickness.

Cut out four circles from the puff pastry using a cookie cutter or a knife (approximately 4-5 inches in diameter).

Place the puff pastry circles on the prepared baking sheet. Prick the pastry with a fork several times to prevent it from puffing up too much.

Top each pastry circle with a generous spoonful of the caramelized onions.

Sprinkle the crumbled goat cheese over the onions.

Bake for 15-20 minutes, or until the pastry is golden brown and the cheese is slightly melted and warmed through.

Let cool slightly before serving.