Prepare the Pastry: Unfold the thawed puff pastry sheet onto a lightly floured surface. Place the pastry sheet on a baking sheet lined with parchment paper. Using a fork, pierce the pastry all over to prevent it from puffing up too much. Bake at 400°F (200°C) for 10 minutes to pre-bake the crust.

Make the Filling: While the pastry bakes, heat the olive oil in a large skillet over medium-high heat. Add the sliced shallot and cook for 2-3 minutes until softened. Add the minced garlic and cook for another 30 seconds until fragrant.

Sauté the Mushrooms: Add the sliced mushrooms to the skillet. Cook, stirring occasionally, for about 5-7 minutes until they have released their liquid and are nicely browned. Stir in the fresh thyme, salt, and pepper.

Finish the Filling: Reduce the heat to low. Stir in the heavy cream or crème fraîche and Parmesan cheese. Cook for 1-2 minutes until the cheese has melted and the mixture is creamy and well-combined. Remove from heat.

Assemble the Tart: Once the pre-baked pastry crust is ready, carefully spoon the mushroom mixture evenly over the top, leaving a small border of pastry around the edges.

Bake the Tart: Brush the exposed pastry edges with the beaten egg wash for a beautiful golden finish. Return the tart to the oven and bake for another 20-25 minutes, or until the pastry is golden brown and the filling is bubbly. Let the mushroom tart cool for a few minutes before slicing and serving.