Preheat your oven to 400°F (200°C).
Heat olive oil in a pan over medium heat, then add onions and sauté until translucent.
Add minced garlic and diced mushrooms to the pan; cook until mushrooms are browned and moisture evaporates.
Stir in thyme, salt, and pepper; remove from heat and let cool slightly.
Roll out the puff pastry on a floured surface, and cut slits along the sides.
Spoon the mushroom mixture down the center of the pastry and sprinkle with Gruyère cheese.
Fold the slits over the filling, alternating sides to create a braid.
Brush the braid with the beaten egg for a golden finish.
Bake the braid in the preheated oven for 25-30 minutes or until golden brown.
Allow the braid to cool slightly before slicing and serving.
