Step 1: Thaw puff pastry according to package directions, ensuring it’s pliable but still cold.
Step 2: In a large, heavy-bottomed skillet or Dutch oven, melt the butter and olive oil over medium-low heat. Add the sliced onions and a pinch of salt.
Step 3: Cook the onions, stirring occasionally, for 45-60 minutes, or until they are deeply golden brown, very soft, and jammy. This slow process coaxes out their natural sweetness.
Step 4: Stir in the minced garlic and cook for another minute until fragrant. Remove from heat and let the caramelized onions cool slightly.
Step 5: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
Step 6: Unroll the thawed puff pastry onto the prepared baking sheet. Using a sharp knife, lightly score a border about 1 inch from the edges of the pastry, without cutting all the way through. Prick the center of the pastry (inside the scored border) several times with a fork.
Step 7: Spread the cooled caramelized onions evenly over the pastry, staying within the scored border.
Step 8: Sprinkle the grated Gruyère cheese generously over the caramelized onions.
Step 9: In a small bowl, whisk the egg with 1 tablespoon of water to create an egg wash. Brush the egg wash along the scored edges of the puff pastry.
Step 10: Bake for 20-25 minutes, or until the puff pastry is puffed, golden brown, and the cheese is melted and bubbly.
Step 11: Remove the tart from the oven and let it cool for 5-10 minutes on the baking sheet before transferring to a cutting board. Garnish with fresh thyme or chives, if desired.
Step 12: Slice into squares or rectangles and serve warm.