Prepare the oven and baking sheet.

1. Preheat the oven to 190°C or 375°F convection, or 200°C or 400°F conventional. Line a rimmed baking sheet with parchment paper.

Brown the mushrooms.

1. In a large skillet over medium heat, heat the butter and olive oil until the butter foams. Add the mushrooms and cook until they begin to release their liquid. Sprinkle with salt and increase the heat to medium-high. Continue cooking, stirring occasionally, until the liquid has evaporated and the mushrooms are deeply browned, about 10 minutes. Leave them undisturbed between stirs to encourage browning.

Add the garlic and herbs.

1. Stir in the garlic and thyme and cook for about 1 minute, until fragrant. Remove from the heat and stir in the parsley. Transfer to a bowl and allow to cool completely. Taste and adjust the salt.

Shape the strudel.

1. On a lightly floured surface, roll the pastry into a rectangle approximately 30 × 25 cm or 12 × 10 inches. Transfer to the prepared baking sheet. Spoon the cooled mushroom filling lengthwise down the centre third, leaving a small border at each end.

Braid the pastry.

1. Using a sharp knife, cut strips approximately 2.5 cm or 1 inch wide along both sides of the filling, leaving the pastry beneath the filling intact. Fold the short ends over the mushrooms, trimming away excess corner pieces if needed. Cross the side strips diagonally over the filling, alternating left and right.

Glaze and bake.

1. Whisk the egg white with the water. Lightly brush over the pastry. Bake until puffed and golden brown, 25–30 minutes.

Rest and Serve

1. Allow the strudel to rest for 10 minutes before slicing. Serve warm, with a green salad if desired.