Line a baking sheet with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, cheeses, salt, red pepper, and paprika at medium speed until combined. Gradually add flour, beating just until combined. Gently shape into 4-inch sticks and place on prepared pan. Refrigerate until firm, about 30 minutes.

Preheat oven to 350°.

Bake until lightly browned, about 12 minutes. Let cool on a wire rack. Store in an airtight container for up to 1 week.