01 - Preheat the oven to 400°F. Line a baking sheet with parchment paper.
02 - Heat butter and olive oil in a large skillet over medium-low heat. Add onions, salt, and sugar. Cook, stirring frequently, for 25–30 minutes until onions are deep golden and caramelized. Stir in thyme and black pepper during the last 5 minutes.
03 - Unroll the puff pastry and cut into 6 equal rectangles. Place on the prepared baking sheet. Using a knife, score a 1/2-inch border around each rectangle, being careful not to cut through.
04 - Brush the scored edges of each pastry rectangle with beaten egg.
05 - Divide caramelized onions evenly within the borders of each pastry rectangle. Top with crumbled goat cheese.
06 - Bake for 15–18 minutes until pastry is golden and crisp with puffed edges.
07 - Remove from the oven and sprinkle with fresh chives or parsley if desired. Serve warm or at room temperature.