Preheat the oven to 350°F. Line 2 baking sheets with parchment paper. Knead the dough with the flour until smooth. On a lightly floured surface, roll out dough until it's about 1/4-inch thick. Make cutouts with a 3-inch tall Z-shaped cookie cutter (see Notes). Reroll the scraps to make more cookies. Place them about an inch apart on the baking sheets and bake until lightly golden around the edges, 10 to 12 minutes. Let cool completely on a wire rack.
Beat confectioner's sugar, egg-white powder, and the water until smooth and thick. Tint the frosting with the blue food coloring until it's the shade you want. Spread the frosting on top of cookies in a thin, even layer, and sprinkle each cookie with decorating sugar immediately.
Z-shaped cookie cutters are available at thecookiecuttershop.com.