Stir the cheese and butter together in a medium bowl to combine. Sift the flour, salt, baking powder, pepper, and cayenne together. Stir into the butter with the water to make a soft dough. Divide the dough into 2 rectangles and wrap each in plastic wrap. Refrigerate until chilled, at least 1 hour and up to 8 hours. (If well chilled, let the dough stand at room temperature for 10 minutes before rolling.)

Position racks in the center and top third of the oven and preheat to 350°F.

Roll out 1 rectangle on a lightly floured work surface into a ¼-inch-thick rectangle about 12 × 7½ inches. Brush the top of the dough with some of the yolk mixture, and sprinkle with 1½ teaspoons of seeds. Using a pizza wheel and a ruler, cut the dough into strips about ¾-inch wide and 3 inches long. Place the strips 1 inch apart on ungreased baking sheets. Repeat with the remaining dough, glaze, and seeds.

Bake until crisp and lightly browned, switching the positions of the baking sheets from top to bottom and front to back halfway through baking, about 20 minutes. Cool on the baking sheets. (The straws can be prepared up to 3 days ahead and stored in airtight containers at room temperature. They can also be frozen, wrapped airtight, for up to 2 months.)