Preheat your oven to 400°F (200°C).
In a large skillet over medium heat, combine olive oil and butter. Add sliced onions, sugar, and season with salt and pepper. Cook for about 20 minutes until caramelized.
Stir in balsamic vinegar and fresh thyme leaves. Remove from heat and let cool slightly.
Roll out the puff pastry on a floured surface and cut into squares (about 3x3 inches).
Place each pastry square on a baking sheet. Spoon caramelized onion mixture onto each square and sprinkle with goat cheese.
Bake for 15-20 minutes until puffed and golden brown.
Let cool slightly before serving warm.