Combine the flour, cheese, salt, and cayenne in a food processor. Process until just blended. Add the butter pieces and pulse until the dough resembles coarse crumbs. Stir the yolk and water together with a fork and drizzle over the mixture. Pulse until the dough begins to form small moist crumbs. Add the chopped nuts and pulse briefly until the crumbs begin to come together.
Pile the moist crumbs on an unfloured work surface. With the heel of your hand, push and gently smear the crumbs away from you until they start to come together in a cohesive dough. Using a pastry scraper or a metal spatula, lift up one edge of the dough and fold it into the center (the dough will still be rough, so don’t expect a neat, smooth fold). Repeat with the opposite edge, like folding a letter. Turn the dough 45 degrees. Give the dough another smearing and shape it into a 14-inch log that’s 1-1/4 inches in diameter. Wrap in plastic and refrigerate until firm, about 4 hours, or up to two days.
Heat the oven to 375°F. Line two large baking sheets with parchment. Using a thin, sharp knife, cut the log into scant 1/4-inch slices. Arrange about 1/2 inch apart on the prepared sheets. Bake until medium to deep golden around the edges, 15 to 20 minutes, rotating the sheets as needed for even baking. If you like, sprinkle the crackers with a little kosher salt just as the baking sheets come out of the oven. Set the sheets on racks to cool. When the coins are completely cool, store them in an airtight container.
The rolled log of dough may be frozen for up to a month and then thawed for about an hour on the counter or in the refrigerator overnight. Or bake the coins ahead, wrap short stacks in plastic, pack the stacks in plastic containers, and stash them in the freezer. Thaw at room temperature (or put the frozen coins right in the oven) and warm them for a few minutes at 325°F to refresh them.