On a lightly floured surface, roll out pastry dough to a 12 1/2-by-9 1/2-inch rectangle; trim edges.
Brush beaten egg over dough until well moistened. Sprinkle 3/4 cup cheese and a pinch of salt over lower half of dough. Fold top half of dough over cheese-covered half. Gently press to seal.
Brush top of dough with beaten egg. Sprinkle with remaining cheese and a pinch of salt, and gently press to adhere. Transfer to a baking sheet lined with parchment paper. Refrigerate 30 minutes.
Preheat oven to 375 degrees. Using a pastry wheel or sharp knife, trim edges, and cut dough into 1/4-by-12-inch strips. Twist into spirals. Space 1/2 inch apart on baking sheets. Press ends onto sheets to prevent straws from straightening. Cover with plastic wrap; refrigerate 30 minutes.
Bake until golden and cooked through, 15 to 16 minutes. Loosen straws from sheets with a thin spatula; transfer to a wire rack to cool.