Preheat the oven to 425 degrees . Line 2 baking sheets with parchment paper. In a medium skillet, heat 2 tablespoons butter over medium heat. Add the mushrooms and cook until they begin to brown, about 4 minutes; set aside to cool.
On a lightly floured surface, roll out the pastry to a 14-inch square, about 1/8 inch thick. Melt the remaining 2 tablespoons butter and brush onto the pastry; sprinkle with 1/2 teaspoon truffle salt and top with the mushrooms, patting them down.
Fold the pastry in half, making a rectangle. Using a rolling pin, roll out the pastry into a 9-by-14-inch rectangle. Brush with the beaten egg and sprinkle with the remaining 1/2 teaspoon truffle salt.
Cut the dough into 3/4-by-9-inch strips and place an inch apart on the prepared baking sheets. Holding the ends of each strip, gently stretch and turn in opposite directions to form long twists. Bake until golden, 10 to 12 minutes; let cool on the baking sheet for 10 minutes, then transfer to a rack to cool completely.