Beat butter at medium speed with a heavy-duty stand mixer until fluffy. Gradually add flour, salt, and red pepper, beating just until combined. Stir in cheese and jalapeño peppers.
Use a cookie press fitted with a bar-shaped disk to shape mixture into long ribbons, following manufacturer's instructions, on parchment paper-lined baking sheets. Cut ribbons into 2-inch pieces.
Bake at 350° for 10 to 12 minutes or until lightly browned. Remove to wire racks to cool.
Jalapeño-White Cheddar Cheese Wafers: Combine ingredients as directed. Roll dough into 3 (9-inch-long) logs. Wrap each log in plastic wrap, and chill 2 hours. Cut each log into 1/4-inch-thick slices, and place on parchment paper-lined baking sheets. Bake at 350° for 12 minutes or until lightly browned.