In a small mixing bowl, stir together the flour, salt, cayenne pepper, and black pepper. Set aside. In the bowl of a stand mixer fitted with the paddle attachment (or with a wooden spoon or your hands in a large bowl), combine the cheese and butter and beat on medium speed until combined. Add the flour mixture and beat on low speed until incorporated. Stop the mixer and scrape down the sides of the bowl with a rubber spatula. Mix in the walnuts on low speed. The dough should be fairly stiff, with small chunks of cheese and walnut visible.

Transfer the dough to parchment paper, waxed paper, or plastic wrap and shape into a log about 1 inch in diameter. Wrap well and freeze until hard, about 2 hours. Or, gather the dough into a ball, flatten into a disk, wrap well in plastic wrap, and chill in the refrigerator until firm but still pliable, about 1 hour.

Preheat the oven to 400F. Line a baking sheet with parchment paper or a nonstick liner.

Unwrap the log and cut crosswise into slices ⅛ to ¼ inch thick. If you have shaped the dough into a disk, unwrap, place on a flour work surface, and roll out into a square or rectangle ⅛ to ¼ inch thick. Using a pizza wheel or sharp knife, cut the dough into 1-inch squares, 1-by-2-inch rectangles, or whatever shape you like. Arrange the crackers on the prepared pan, spacing them about 1 inch apart.

Bake the crackers until golden brown on the edges and lighter in the center, 7 to 10 minutes, depending on size and thickness. Transfer to a wire rack and let cool completely.