How to Make It
In a food processor, pulse the butter with the Gouda, cheddar, cayenne, salt and black pepper until the butter is coarsely chopped and the mixture forms small clumps. Add the flour and pulse until large moist clumps form.
Turn the clumps out onto a work surface and knead gently until the dough comes together. Divide the dough in half and press each half into disks. Roll out each disk between 2 sheets of wax paper to about 1/4 inch thick. Slide the wax paper–covered disks onto a baking sheet and freeze for at least 1 hour, until very firm.
Preheat the oven to 350° and line 2 large baking sheets with parchment paper. Working with one piece of dough at a time, peel off the top sheet of wax paper. Using a 1 1/2-inch round cookie cutter, stamp out the cookies as close together as possible. Arrange the cookies 1 inch apart on the prepared baking sheets.
Bake the cookies for about 20 minutes, until they are lightly golden and just firm; shift the baking sheets from top to bottom and front to back halfway through. Let the cookies cool on the baking sheets for 3 minutes, then transfer them to a wire rack to cool completely.