Let's bring out the food processor for this one, it makes things so much easier. Pop your flour, salt, cayenne pepper, and paprika into the bowl and pulse it until everything is mixed well. Now, add both of your cheeses and process it again until the mixture looks like coarse meal.
Next, add your butter. Process it all until a proper dough starts to form.
Turn that lovely dough out onto your counter and divide it in two. Gently roll each piece into a log, about 10 to 12 inches long and roughly an inch and a quarter wide.
Wrap each log up snug in plastic wrap and tuck them into the refrigerator. They need to chill for at least 3 to 4 hours to firm up, this helps them slice beautifully later!
When you are ready to bake, warm your oven to 350°F. Line two large baking sheets with parchment paper so nothing sticks.
Unwrap your chilled logs and carefully cut them into slices, about a quarter-inch thick. Place these little rounds on your baking sheets, leaving about half an inch of space between them.
Bake them until they are a beautiful golden brown, which should take about 25 minutes. It helps to rotate the pans halfway through so they bake evenly.
Let the coins cool on the sheets for 5 minutes to set, then move them to wire racks to cool completely.