►Position oven racks in the top and bottom third of oven. Preheat oven to 375°F. Butter two baking sheets or line them with silicone baking liners or parchment paper.
►Combine flour, salt, onion powder, and cayenne in a food processor fitted with a metal blade and pulse to combine. Add butter and cheese and process until almost smooth. Add chopped pimentos and pulse a few times. Transfer dough to a clean bowl and finish incorporating pimentos into the dough by hand. (If you use the food processor it will purée the pimentos and you’ll wind up with orange dough.)
►Transfer dough to a clean work surface. To shape dough, work it in your hands; it should be soft and pliable (like Play-Doh). Shape dough into two equal cylinders and wrap tightly in plastic wrap. Transfer to refrigerator and chill until firm, about 30 minutes.
►Remove chilled dough from refrigerator. Then, working with 1 cylinder at a time, using a utility knife, cut into ¼-inch-thick slices and place 1 inch apart on the prepared baking sheet. Repeat with remaining dough. Any remaining scraps can be re-shaped into cylinders, chilled again, and cut into slices.
►Bake cheese straws, rotating the baking sheets once, until lightly browned on the edges, about 20 minutes. Transfer baking sheets to a rack to cool slightly. Using an offset or slotted spatula, remove the individual shortbreads to a rack and cool completely.
►Store the cheese straws at room temperature in an airtight container between sheets of waxed paper. They will keep for 2 to 3 weeks.