Start by heating olive oil in a skillet over medium-low heat. Add your sliced onions with a pinch of salt and stir occasionally. Cook slowly for about 15-20 minutes until they’re soft, golden brown, and caramelized. Remove from the heat and set aside to cool.
Roll out the puff pastry into a 10x10-inch square on parchment paper. If using store-bought pastry, thaw it thoroughly and trim any uneven edges.
Lightly score a 1-inch border around the edges to create a crust. This border will puff up as it bakes to frame your tart.
Brush the border of the pastry with egg wash to ensure a golden, crisp crust. Spread the Greek yogurt evenly over the center of the pastry, steering clear of the edges. Sprinkle freshly grated Parmesan over the yogurt for a cheesy layer of flavor.
Top the yogurt mixture with your cooled caramelized onions, spreading them evenly across the center. Sprinkle thyme leaves on top, and season generously with salt and pepper.
Preheat your oven to 400°F (200°C). Slide the parchment paper and tart onto a baking sheet, then bake for 20-25 minutes. The pastry should be golden brown and puffed around the edges. Once baked, cool the tart for 10 minutes before slicing and serving.