1. In a food processor, pulse both flours, baking powder, salt, cheese and cayenne until mixed. Add butter; pulse until crumbly and mixture resembles texture of small peas, about 10 seconds. Beat yolk with 1/4 cup cold water; add to processor. Pulse several times until dough starts to come together, about 20 seconds. Dough should not be sticky, but should just hold together. Pulse in a few drops of cold water, if needed. Transfer to a lightly floured work surface; gather into a ball. Divide dough in half, flatten each into a 4-by-5-inch rectangle and wrap in plastic. Chill for at least 30 minutes and up to 2 hours. Remove 1 piece of dough from refrigerator. Let soften slightly before rolling.
2. Preheat oven to 400°F. Lightly flour a sheet of parchment. Working with 1 piece at a time, roll dough on parchment into a 1/8-inch-thick sheet, about 8 by 12 inches. Gently slide parchment onto a baking sheet. Using a pastry wheel or sharp knife, cut dough into 1 1/4-inch squares, trimming and discarding uneven edges, if desired. Prick each square with a fork. Bake until crackers are lightly browned around edges and dried out in center, about 12 minutes. With a small, sharp knife, recut any crackers that have baked together. Let cool on baking sheet on a wire rack, then carefully pull apart any squares that are stuck together. Repeat with remaining dough. Store in an airtight container.