In a large skillet, heat 2 tablespoons of olive oil and 1 tablespoon of butter over medium heat. Add 3 thinly sliced yellow onions, 1 tablespoon of sugar, and a pinch of salt and pepper. Sauté undisturbed for about 15 minutes until golden brown. Stir in 1 tablespoon of balsamic vinegar and 1 teaspoon of thyme, cooking for an additional 5 minutes until jammy.

Preheat your oven to 400°F (200°C). Roll out the thawed puff pastry on a floured surface and cut into 6 equal rectangles. Arrange on a parchment-lined baking sheet. Spread caramelized onion mixture over each rectangle, leaving a small border. Crumble goat cheese on top and sprinkle with additional thyme.

Bake for about 15 minutes, checking every 2 minutes to avoid over-browning. Look for a golden, puffed pastry.

Once baked, let the tarts cool slightly for 5 minutes before serving. They can be reheated in a preheated oven at 350°F (175°C) for 5-7 minutes.