Step 1: Heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium-low heat. Add the thinly sliced onions and a pinch of salt. Cook slowly, stirring occasionally, for 30-45 minutes, or until the onions are deeply golden brown and very soft. This is the crucial step for the caramelized onion mushroom cheese puff pastry braid; don’t rush it! If desired, add the balsamic vinegar during the last 5 minutes of cooking for extra depth of flavor. Remove onions from the skillet and set aside to cool.
Step 2: In the same skillet, melt 1 tablespoon of butter over medium-high heat. Add the sliced mushrooms and cook, stirring occasionally, until they release their liquid and turn golden brown, about 7-10 minutes. Add the minced garlic and fresh thyme, and cook for another minute until fragrant. Season with salt and pepper. Remove from heat and combine with the cooled caramelized onions.
Step 3: Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
Step 4: On a lightly floured surface, unroll the thawed puff pastry sheet. Gently roll it out slightly to about a 10×14 inch rectangle.
Step 5: Using a sharp knife or pizza cutter, make cuts inward on both long sides of the pastry, about 1 inch apart and extending about 1/3 of the way into the pastry. You should have a solid strip down the center and diagonal strips on each side.
Step 6: In a small bowl, combine the shredded Gruyère and mozzarella cheeses.
Step 7: Spread the caramelized onion and mushroom mixture down the center solid strip of the puff pastry. Top generously with the mixed cheeses.
Step 8: To create the braid, fold one diagonal strip from one side over the filling to the opposite side. Then, take a diagonal strip from the other side and fold it over, overlapping the previous strip. Continue alternating strips, creating a braided pattern over the filling, until you reach the end. Gently tuck the ends underneath. This creates the beautiful form of your caramelized onion mushroom cheese puff pastry braid.
Step 9: Carefully transfer the braided puff pastry to the prepared baking sheet.
Step 10: Brush the entire surface of the braid with the beaten egg wash. This will give your caramelized onion mushroom cheese puff pastry braid a beautiful golden shine.
Step 11: Bake for 20-25 minutes, or until the pastry is puffed, golden brown, and the cheese is melted and bubbling.
Step 12: Let the caramelized onion mushroom cheese puff pastry braid cool for 5-10 minutes before slicing and serving. This allows the filling to set slightly. Enjoy your delicious homemade caramelized onion mushroom cheese puff pastry braid!