Preheat oven to 400°F (200°C). Line a large baking sheet with parchment paper.

In a large skillet over medium heat, melt butter with oil. Add diced onion and sauté until soft and translucent, about 5 minutes.

Add sliced mushrooms to the skillet. Cook until moisture is released and mushrooms are golden brown, about 8-10 minutes.

Stir in minced garlic, thyme, salt, and pepper. Pour in white wine and simmer until liquid has completely evaporated.

Remove from heat and stir in fresh parsley. Transfer to a plate and let cool for 5-10 minutes.

On a lightly floured surface, roll puff pastry into a rectangle approximately 10 by 14 inches. Transfer to prepared baking sheet.

Optional: Spread a thin line of whole grain mustard down the center third of the pastry. Spoon cooled mushroom filling down the center third, leaving an inch clear at top and bottom. Sprinkle shredded Gruyere evenly over mushrooms.

Cut diagonal strips about 1 inch wide along both outer sides of the pastry. Fold top and bottom edges over filling, then alternate folding side strips over the center in a crisscross pattern to create a braid.

Brush entire braid with beaten egg wash. Sprinkle with seeds if desired.

Bake for 25-30 minutes until pastry is puffed and deep golden brown.

Let rest for 5 minutes before slicing with a sharp serrated knife.