Combine flour, salt, cayenne and paprika in a food processor until well combined. Add both cheese and process until dough resembles coarse meal. Add the butter and process until a dough forms.

Remove dough from processor onto counter and form into two 10-12 inch logs about 1-1/4 inch in diameter. Wrap each log in plastic wrap and chill in refrigerator for at least 3-4 hours. (Dough can also be stored in the freezer for up to one month. I like to wrap mine in plastic wrap and add to a Ziploc freezer bag if storing in freezer.)

Preheat oven to 350 degrees. Line two large baking sheets with parchment paper. Unwrap logs and cut into 1/4 inch thick rounds and place on prepared sheets 1/2 inch apart.

Bake until golden bown, about 25 minutes, rotating sheets at the halfway point of baking. Let coins cool on sheets for 5 minutes before moving to wire racks to cool completely. Coins can be stored at room temperature in an airtight container for up to 3 days.