Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Heat the butter and olive oil in a skillet over medium heat.
Add the mushrooms and cook for 6–8 minutes until their moisture evaporates and they become lightly golden.
Stir in the shallot, garlic, salt, pepper, and thyme. Cook for another 1–2 minutes until fragrant.
Remove from the heat and allow the filling to cool for about 10 minutes.
Roll the puff pastry into a rectangle on a lightly floured surface and transfer it to the prepared baking sheet.
Lightly score the center third lengthwise without cutting through. Slice diagonal strips approximately 1 inch wide along both sides.
Spoon the mushroom filling into the center and evenly sprinkle the Gruyère cheese over the top.
Fold the pastry strips alternately across the filling to create the signature Mushroom Puff Pastry Braid pattern.
Brush the entire braid with the beaten egg.
Bake for 22–28 minutes, or until deeply golden, puffed, and crisp.
Let cool for several minutes before slicing and serving.