Step 1: Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats.
Step 2: In a large mixing bowl, or the bowl of a stand mixer with the paddle attachment, cream together the softened unsalted butter and freshly grated sharp cheddar cheese until light and fluffy, about 2-3 minutes.
Step 3: Add the all-purpose flour, cayenne pepper, and salt to the butter and cheese mixture. Beat on low speed until the mixture just comes together to form a soft, cohesive dough. Do not 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 into a rectangle about 1/8 to 1/4 inch thick. Aim for an even thickness.
Step 5: Using a sharp knife or a pizza cutter, trim the edges to create a neat rectangle. Then, cut the dough into strips about 1/4 to 1/2 inch wide and 3-4 inches long.
Step 6: Carefully transfer the cut cheese straws to the prepared baking sheets, leaving a small space between each one.
Step 7: Bake for 12-18 minutes, rotating the baking sheets halfway through, until the cheese straws are golden brown and crisp. Watch them closely as they can brown quickly.
Step 8: Remove the cheese straws from the oven and transfer them immediately to a wire rack to cool completely. They will crisp up further as they cool. Serve at room temperature or store in an airtight container.