On a lightly floured surface, roll out pastry dough to a 9-by-20-inch rectangle. Sprinkle 3/4 cup cheese over center of dough. Starting at the near short end, fold dough into thirds, enclosing cheese. Wrap in plastic; refrigerate 1 hour. Repeat. Wrap in plastic; refrigerate at least 4 hours or overnight.
Cut dough in half; wrap half in plastic, and refrigerate. On a lightly floured surface, roll out half the dough to a 12-by-15-inch rectangle about 1/8 inch thick. (Do not press too hard on edges.)
Using a pastry brush, dust off excess flour; brush beaten egg over dough until well moistened. Sprinkle 1/2 cup plus 2 tablespoons cheese and a pinch of salt over lower half of dough. Fold top half over cheese-covered half. Gently press to seal. Brush top of dough with beaten egg; sprinkle with remaining 1/2 cup plus 2 tablespoons cheese and a pinch of salt.
Trim dough to 12 by 6 1/2 inches with a pastry wheel or knife. Transfer to a baking sheet lined with parchment paper. Refrigerate 30 minutes. Repeat with remaining dough, cheese, and salt.
Preheat oven to 375 degrees. Using a pastry wheel, cut dough into 3/8-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, about 18 minutes. Loosen straws from sheets with a thin spatula; transfer to a wire rack to cool. Store in airtight containers at room temperature up to 1 day.