Preheat the oven to 400°F and line a baking sheet with parchment paper.
In a skillet, heat olive oil and butter over medium heat.
Add mushrooms and onion. Cook until softened and golden, about 7 minutes.
Stir in garlic, thyme, salt, and pepper. Cook 1 more minute, then remove from heat.
Roll out puff pastry on a lightly floured surface. Place the mushroom mixture down the center.
Sprinkle Gruyere cheese over the mushrooms.
Cut strips along both sides of the pastry and braid them over the filling.
Brush the top with egg wash for that golden finish.
Bake for 20–25 minutes until puffed and deeply golden brown.
Cool slightly before slicing and serving.