Preheat your oven to 350°F (180°C) and prepare a baking sheet lined with parchment paper.

Melt 2 tablespoons of unsalted butter and 1 tablespoon of olive oil in a skillet over medium heat. Add 1 finely diced yellow onion and sauté for about 5 minutes.

Stir in 2 minced garlic cloves and 8 ounces of finely chopped cremini mushrooms. Cook for around 8 minutes until browned.

Fold in 4 ounces of cream cheese, 1/4 cup of grated Parmesan cheese, and 1 teaspoon of Dijon mustard. Stir in 1 cup of shredded Gruyère cheese until melted.

Roll out a sheet of puff pastry into a rectangle and cut 8 diagonal strips along each side, leaving a wide center strip.

Spread the mushroom filling in the center, fold edges over the filling and braid the strips on top.

Transfer the braid to the baking sheet and brush with a beaten egg. Bake for 20 to 22 minutes until golden-brown.

Let the braid cool for about 10 minutes, then garnish with freshly chopped parsley and serve.