Step 1: Melt 2 tablespoons of butter in a large skillet or Dutch oven over medium-low heat. Add the thinly sliced yellow onions. Cook, stirring occasionally, for 30-45 minutes, or until the onions are deeply golden brown and very tender. Season with a pinch of salt and pepper in the last 10 minutes of cooking. Let cool slightly.
Step 2: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper. Unfold the thawed puff pastry onto the prepared baking sheet. Lightly score a border about 1/2 inch from the edge of the pastry with a sharp knife, being careful not to cut all the way through. Prick the center area inside the border a few times with a fork.
Step 3: Spread the cooled caramelized onions evenly over the center of the puff pastry, staying within the scored border. Sprinkle the 1 cup of freshly grated Gruyere cheese over the onions.
Step 4: In a small bowl, whisk together the large egg and 1 tablespoon of water to create an egg wash. Brush the scored edges of the puff pastry with the egg wash.
Step 5: Bake the tart for 20-25 minutes, or until the puff pastry is puffed, golden brown, and the cheese is melted and bubbly. Rotate the baking sheet halfway through baking for even browning.
Step 6: Remove the tart from the oven and let it cool on the baking sheet for 5-10 minutes before slicing and serving. Garnish with fresh thyme or chives, if desired.