Preheat your oven to 350°F (175°C) and line a baking tray with parchment paper.

In a skillet, combine olive oil and unsalted butter over medium heat. Add diced onion and sauté for about 5 minutes until softened.

Add minced garlic and sliced mushrooms to the skillet. Sauté for around 8 minutes until mushrooms are browned.

Stir in thyme, salt, black pepper, and optional white wine. Cook until the liquid is absorbed.

Incorporate cream cheese, Parmesan cheese, and optional Dijon mustard. Mix well and fold in Gruyère cheese.

Beat one egg and mix it into the filling. Allow the mixture to cool slightly.

Roll out the thawed puff pastry into a rectangle. Cut diagonal strips about 1 inch apart along the sides.

Spread filling down the center of the puff pastry. Fold ends over the filling and braid the strips over the top.

Brush the pastry with the remaining beaten egg. Bake in the preheated oven for 20-22 minutes until golden brown.

Let cool for 10 minutes, garnish with parsley, slice, and serve warm.