Prepare the Onions:

1. Caramelize the Onions: In a large skillet, heat the olive oil and butter over medium heat. Add the sliced onions, season with a pinch of salt, and cook slowly for about 20-25 minutes, stirring occasionally, until the onions are golden brown and caramelized.
2. Sweeten and Flavor the Onions: Once the onions are caramelized, stir in the sugar and balsamic vinegar. Cook for an additional 3-5 minutes until the vinegar has reduced and the onions are glossy. Stir in fresh thyme leaves, if using. Remove from heat and set aside to cool.

Prepare the Puff Pastry:

3. Preheat the Oven: Preheat your oven to 375°F (190°C).
4. Roll Out the Pastry: Roll out the puff pastry on a lightly floured surface until it is large enough to fit your tart pans or baking dish. If using individual tart pans, cut the pastry into circles slightly larger than the pans.
5. Assemble the Tarts: If using a tart pan, place the cooled caramelized onions in the bottom, spreading them evenly. Sprinkle the grated Gruyère cheese on top of the onions. Place the puff pastry over the onions and cheese, tucking the edges into the sides of the pan to form a crust.

Bake the Tarts:

6. Apply Egg Wash: Brush the top of the pastry with a beaten egg for a golden, glossy finish once baked.
7. Bake the Tarts: Place the tarts in the preheated oven and bake for 25-30 minutes, or until the puff pastry is golden brown and crisp.

Flip and Serve:

8. Flip the Tarts: Remove the tarts from the oven and allow them to cool for a few minutes. Carefully flip the tarts onto a serving plate or platter. The caramelized onions should be on top, forming a beautiful, golden layer.
9. Serve: Slice and serve warm, garnished with a few fresh thyme sprigs if desired.