Preheat oven to 350°. Beat Cheddar cheese, next 6 ingredients, and, if desired, red pepper at medium speed with a heavy-duty electric stand mixer until blended. Gradually add flour, beating at low speed just until combined.
Turn dough out onto a well-floured surface. Divide dough in half; flatten each half into a square. Roll each square to 1/8-inch thickness (about 12 x 12 inches). Cut into 1/2- x 12-inch strips, using a fluted pastry wheel.
Holding 1 dough strip at each end, twist strip until tightly curled. Pinch ends to seal. Repeat with remaining strips, and place 1/2 inch apart on 2 parchment paper-lined baking sheets.
Bake at 350° for 10 minutes, placing 1 sheet on middle oven rack and 1 sheet on lower oven rack. Rotate pans front to back, and top rack to bottom rack. Bake 10 to 12 more minutes or until edges begin to brown. Cool on baking sheets on wire racks 5 minutes. Remove to wire racks, and cool completely.