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

In a skillet, combine olive oil and butter over medium heat. Sauté diced onion until translucent, about 5 minutes.

Add minced garlic and sliced cremini mushrooms to the skillet, cooking until browned, about 8 minutes.

Stir in thyme, salt, and pepper. If using white wine, add now and reduce.

Remove from heat, mix in cream cheese and Parmesan until melted, then fold in Gruyère.

Beat one egg and mix into the cooled filling mixture.

Roll out puff pastry sheets and cut diagonal strips along the sides, leaving the center open.

Spoon the filling onto the center of the pastry, fold ends and braid the strips over the filling.

Transfer to the baking tray, brush with the remaining beaten egg, and bake for 20-22 minutes until golden.

Allow to cool for 10 minutes before slicing and garnish with parsley.