In a skillet, melt 2 tablespoons of unsalted butter and add 1 tablespoon of olive oil over medium heat. Add ½ sliced onion with a pinch of salt and pepper and caramelize for 10-15 minutes.

Roll out 2 sheets of thawed puff pastry on a lightly floured surface and cut into 3-inch circles. Place them on a baking sheet lined with parchment paper.

Layer thinly sliced tomatoes onto the center of each pastry round, slightly overlapping them. Spoon caramelized onions over the tomatoes and sprinkle shredded cheese on top.

Whisk together 1 large egg and 1 teaspoon of water to create an egg wash. Brush around the edges of each pastry circle.

Preheat the oven to 400°F (204°C) and bake the tarts for 16-20 minutes until puffed and golden brown.

Let the tarts cool slightly and optionally garnish with fresh parsley or herbs before serving.