Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
Whisk together flour, salt, paprika, and cayenne in a large bowl.
Add cold butter cubes and blend with fingers or a pastry cutter until the mixture resembles coarse crumbs.
Stir in shredded cheddar cheese evenly.
Add 2 tablespoons cold water and mix until dough begins to come together. Add more if necessary.
Form dough into a disk, wrap and chill for 20 minutes.
Roll dough to 1/4-inch thickness. Cut into 1/2-inch strips.
Twist each strip and place on prepared baking sheet.
Bake for 12 to 15 minutes or until golden and crisp. Cool on a wire rack.