Preheat your oven to 350°F (180°C) and line a baking tray with parchment paper.

In a large skillet over medium heat, add the olive oil and unsalted butter. Once the butter has melted, add the diced yellow onion and sauté until softened and translucent.

Add the minced garlic and sliced cremini mushrooms, cooking until the mushrooms are golden brown and tender.

Stir in fresh thyme, salt, black pepper, and the dry white wine if using, cooking until most of the wine has evaporated. Remove from heat and let cool slightly.

Mix in cream cheese and Parmesan until creamy, then fold in Gruyère cheese and one beaten egg.

Roll out puff pastry sheet, cut diagonal strips on each long side, and spoon the mushroom mixture down the center. Braid the strips over the filling.

Transfer to the baking tray and brush the top with beaten egg. Bake for 20-22 minutes until golden brown.

Let cool for about 10 minutes on a wire rack before serving warm.