Start by heating a large skillet over medium heat. Add 1 tablespoon of olive oil and 1 tablespoon of butter to the pan. Allow the butter to melt, swirling the pan to combine the oils.

Add 3-4 thinly sliced yellow onions to the skillet, stirring them into the warm oil and butter. Sprinkle in 1 tablespoon of sugar, and season with salt and pepper. Let the onions cook undisturbed for 5 minutes.

Stir occasionally for about 15 more minutes, until they turn a beautiful golden brown and become soft and jammy.

Once your onions are caramelized, pour in 1 tablespoon of balsamic vinegar and add a few sprigs of fresh thyme. Stir well and cook for an additional 5 minutes.

Preheat your oven to 400°F (200°C). Roll out 1 sheet of puff pastry on a lightly floured surface to about 1/8 inch thick.

Using a sharp knife, cut the pastry into rectangles or squares, leaving a small border around each piece. Place them on a lined baking tray.

Spread a generous spoonful of the caramelized onion mixture over each pastry square, ensuring you stay within the borders. Crumble approximately 4-6 ounces of goat cheese over the onions.

Bake for 15 minutes, checking every 2 minutes after the 12-minute mark until they are golden and puffed up.

Once baked, remove the tarts from the oven and let them cool on the tray for about 5 minutes before serving warm.