In a large skillet, heat 2 tablespoons of olive oil and 2 tablespoons of butter. Add the finely chopped shallot and sauté for 3-5 minutes until soft. Stir in minced garlic and cook for 1 minute.

Add 1 pound of mixed mushrooms to the skillet. Cook for 8-10 minutes until browned and moisture evaporates.

Pour in 1/4 cup of dry white wine to deglaze, scraping up bits from the bottom. Simmer for 2 minutes.

Stir in 1/4 cup heavy cream, 1 teaspoon fresh thyme, and 1/4 teaspoon nutmeg. Season with salt and pepper, simmering for 5 minutes.

Remove from heat and fold in half of the 8 ounces of grated Gruyere cheese until melted. Cool slightly.

Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

Roll out thawed puff pastry into a 12x16 inch rectangle on a floured surface. Cut in half lengthwise.

Place one rectangle on the baking sheet. Spread mushroom filling evenly, leaving a border.

Sprinkle remaining Gruyere cheese over the filling. Cover with the second pastry rectangle and seal edges.

Whisk together 1 beaten egg and 1 tablespoon of milk or water. Brush egg wash over the pastry and score slits on top.

Bake for 20-25 minutes until puffed and golden brown.

Let cool slightly before slicing and serve warm or at room temperature.