Preheat oven to 350?F (180?C). Line a large baking tray with parchment paper and set aside.

In a large skillet over medium to high heat, add the olive oil and onions. Cook until soft, about 5 minutes.

Add the mushrooms and garlic to the onions and stir. Cook until the mushrooms are soft and browned, about another 5-8 minutes.

Reduce heat to low and add the cream cheese, parmesan cheese, oregano, salt, pepper, and parsley. Stir until combined and creamy. Remove from heat.

Add one of the whisked eggs to the mixture and stir until fully incorporated.

Unroll the puff pastry on parchment paper. Cut approximately 8 equal diagonal strips on each side and cut the top corners off with a small oval cut at the top.

Spread the mushroom filling down the center of the pastry, leaving a 1/2 inch (1 cm) space at the top and bottom. Fold the pastry over the filling and fold the strips over each other. Press down the edges to seal.

Lift the parchment paper onto the baking tray. Brush the top of the pastry braid with the remaining whisked egg.

Bake for 20-22 minutes until golden and puffed up.

Remove from oven and let cool for 10 minutes before cutting into slices and serving hot.