Put the cold butter, Gouda, cheddar, salt, black pepper, and cayenne in a food processor and pulse until the butter is in bits and the mixture forms small curds. Add the flour and pulse again, in long pulses, until the dough is moist and forms larger, popcorn-like curds.
Turn the dough out and knead it gently, just until you can shape it into a ball. Divide the dough in half and pat each half into a disk.
Working with one disk at a time, roll to a thickness of 1/4 inch. Place each slab between two pieces of parchment paper and chill for 4-5 hours
When ready to bake, preheat your oven to 350 degrees F. LIne a baking sheet with parchment or a silicone baking mat.
Working with one piece of dough at a time, use a 1.5 inch-diameter cookie cutter to cut as many cookies as possible from each slab of dough and place them on the lined baking sheet.
Gather the scraps, re-roll, chill for 10 minutes, cut, and so on, until you've used all your dough.
Bake the cookies for 16 to 18 minutes, rotating the baking sheets after 9 minutes, or until they're lightly golden on top and more golden on the bottom. Let the cookies rest on the baking sheet for a couple of minutes, then transfer them to a rack and cool completely.
From Dorie Greenspan's Dorie's Cookies. Makes about 45 cookies.