In a food processor, combine butter, gouda, cheddar, salt, pepper and cayenne pepper. Pulse until the butter and cheese are chopped into the size of rice. Add flour and pulse until the mixture is moist and comes together like large crumbles. Transfer the dough to a clean working surface. Combine and shape into a ball. Divide the dough into 2 parts and pat into disks.

Place 1 disk between 2 parchment papers. Using a rolling pin, roll into ¼-thick. Transfer to a baking sheet. Repeat with the other disk and place on top of the other sheet of dough. Chill in the freezer for 1 hour.

Preheat oven to 350˚F (177˚C). Line a baking sheet with a parchment paper.

Once the dough is chilled, remove 1 sheet from the freezer. Peel both parchment papers off. Place one of the parchment papers on a clean working surface and put the dough on top. With a 1½-inch round cookie cutter, cut out as many cookies as you can. Line them on the prepared baking sheet and space the dough apart for 1 inch. Collect the leftover scraps and keep in the fridge.

Bake the cookies for 16 – 18 minutes, rotating the baking sheets after 9 minutes. Bake until the cookies are light golden brown on top and deep golden brown on bottom. Transfer the baking sheets to counter and let the cookies rest on the sheets for 2 minutes. Transfer the cookies to a cooling rack to cool completely.

Repeat with the remaining dough. Gather the scarps and combine with the scraps in the fridge. Roll into a ball and pat into a disk. Roll the dough into ¼-inch thickness just like before. Chill in the freezer for 1 hour. Cut and bake.