Step 1: Prepare the Puff Pastry

• Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
• Roll out the puff pastry on a floured surface until it’s about 1/4 inch thick. Transfer it to the prepared baking sheet.
• Using a knife, gently score a border about 1 inch from the edge, being careful not to cut all the way through. This will create a raised crust.

Step 2: Make the Mushroom and Spinach Filling

• Heat 2 tablespoons of olive oil in a large skillet over medium heat.
• Add the thinly sliced onions and cook until they are softened and caramelized, about 10 minutes.
• Stir in the minced garlic and cook for another 1 minute until fragrant.
• Add the mixed mushrooms and sauté until they release their moisture and start to brown, about 5-7 minutes.
• Toss in the fresh spinach and cook until wilted, about 2 minutes.
• Season the mixture with salt and black pepper. Remove from heat and set aside.

Step 3: Assemble the Tart

• Spoon the mushroom and spinach mixture onto the puff pastry, spreading it evenly within the scored border.
• Brush the edges of the puff pastry with the beaten egg for a golden crust.
• Bake the tart in the preheated oven for 20-25 minutes, or until the puff pastry is golden and crispy.

Step 4: Prepare the Hazelnut Pesto

• While the tart is baking, prepare the pesto. In a food processor, combine toasted hazelnuts, fresh basil leaves, Parmesan cheese, and garlic cloves.
• Pulse until the ingredients are finely chopped.
• Gradually add the olive oil while the processor is running, until the pesto reaches a smooth consistency.
• Stir in the lemon juice and season with salt and pepper to taste.

Step 5: Finish the Tart

• Once the tart is done baking, remove it from the oven and let it cool for 5 minutes.
• Tear the burrata cheese and place it on top of the tart.
• Drizzle generously with the toasted hazelnut pesto.
• Slice and serve immediately.