6 ounces hard or semi-firm cheese, such as Gruyére, Parmesan, Manchego, or extra sharp Cheddar
All-purpose flour (for dusting)
1 14- or 17-ounce package frozen puff pastry, thawed overnight in refrigerator
1 large egg yolk
1 teaspoon sweet paprika, divided
¼ teaspoon cayenne pepper, divided
Freshly ground black pepper
Grate 6 oz. cheese on the medium holes of a box grater. Line 2 baking sheets with parchment paper. Arrange racks in upper and lower thirds of oven; preheat to 400°.
Dust work surface lightly with flour and unfold or unroll puff pastry on surface. Roll out lightly with a rolling pin to smooth creases, then cut pastry in half crosswise. (If you’re using a brand of puff pastry that comes with 2 sheets instead of 1, just roll out each piece lightly but don’t cut.)
Mix 1 egg yolk and 1 tsp. water with pastry brush in a small bowl. Lightly brush egg wash across surface of 1 piece of pastry.
Sprinkle half of grated cheese all over egg-washed surface in an even layer.
Using your fingertips and holding your hand at least 8" above the surface, sprinkle ½ tsp. paprika, then ⅛ tsp. cayenne over cheese. Season with salt (go easy if you’re already using a salty cheese like Parm), then very generously season with black pepper.
Place second sheet of puff pastry over top, aligning edges, and press gently to flatten. Lightly brush surface of second sheet with more egg wash.
Sprinkle with remaining cheese, paprika, and cayenne; season with salt and pepper.
Dust rolling pin with a bit more flour. Gently roll over top of pastry (yes, you’re rolling directly over the cheese). If bottom layer of pastry starts to stick, dust underneath with more flour, or if rolling pin starts to stick to cheese, dust pin with more flour. Roll pastry out to a long rectangle just under ¼" thick. The dimensions aren’t important but try to keep the rectangle under a foot in length (otherwise, the straws will be too long to handle).
Using your knife, cut rectangle into ½"-thick strips. For fewer straws that are longer, cut lengthwise. For more straws that are shorter (and easier to handle), cut crosswise.
Working one strip at a time, transfer to prepared sheets and twist 2 ends in opposite directions several times. Repeat, spacing twists about 1" apart, until you’ve used all the pastry and filled both sheets.
Bake cheese straws, rotating pans once top to bottom and front to back, until golden brown and cheese is toasted and crisp, 12–18 minutes. Let cool completely on sheets. Carefully remove from parchment and serve
Do Ahead: Unbaked twists can be made 1 month ahead. Wrap tightly in plastic on baking sheet and freeze. Bake directly from freezer without thawing (increase bake time by several minutes).