Step 1: Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper.
Step 2: In the bowl of a stand mixer fitted with the paddle attachment (or a large bowl with a hand mixer), combine the softened unsalted butter and freshly grated sharp cheddar cheese. Beat on medium speed until well combined and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 3: Add the all-purpose flour, salt, cayenne pepper (if using), and black pepper to the butter and cheese mixture. Beat on low speed until the mixture comes together to form a soft, cohesive dough. Be careful not to overmix.
Step 4: Divide the dough in half. On a lightly floured surface or between two sheets of parchment paper, roll out one half of the dough to a thickness of about 1/8 inch. Aim for an even thickness.
Step 5: Using a pizza cutter or a sharp knife, trim the edges of the dough to form a rectangle. Then, cut the dough into strips about 1/2 inch wide and 3-4 inches long. You can gently twist each strip once or twice before placing it on the baking sheet, if desired.
Step 6: Carefully transfer the cut cheese straw strips to the prepared baking sheets, leaving a small space between each one.
Step 7: Bake for 12-15 minutes, or until the cheese straws are golden brown and firm to the touch. Let them cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely. They will crisp up further as they cool. Repeat with the remaining dough.