Tartelettes aux Oignons Caramelisés (Caramelized Onion Tartlets)

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

In a large skillet over medium heat, melt butter and olive oil. Add onions and cook, stirring occasionally, until softened and translucent, about 10 minutes.

Reduce heat to low. Add brown sugar, balsamic vinegar, thyme, salt, and pepper. Cook, stirring occasionally, until onions are deeply caramelized and very soft, about 20-25 minutes. Stir frequently towards the end to prevent burning.

While onions are caramelizing, unfold puff pastry on a lightly floured surface. Using a 4-inch cookie cutter or a knife, cut out 6 circles from the pastry.

Place pastry circles on the prepared baking sheet. Brush the edges of each circle with beaten egg (egg wash).

Spoon caramelized onions evenly onto the center of each pastry circle, leaving a small border around the edge.

Sprinkle crumbled goat cheese over the caramelized onions.

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

Let cool slightly before serving. Garnish with fresh thyme sprigs, if desired.