Royal Icing: In the bowl of an electric mixer fitted with the paddle attachment, beat confectioners' sugar, meringue powder, and 2/3 cup water on low speed until smooth, about 7 minutes. Icing should be the consistency of glue. (If icing is too thick, mix in a little more water. If icing is too thin, add more confectioners' sugar.) Use immediately, or store in an airtight container in refrigerator up to 1 week. Stir before using.

Cookies: Sift together flour, baking powder, and salt in a bowl. In the bowl of an electric mixer fitted with paddle attachment, beat together butter and granulated sugar on medium speed until pale and fluffy, about 3 minutes. Beat in eggs and vanilla. Reduce speed to low; gradually mix in flour mixture. Divide dough in half; shape each half into a flat disk and wrap in plastic. Refrigerate until firm, at least 1 hour or overnight.

Preheat oven to 325 degrees, with racks in upper and lower thirds. Let one disk stand at room temperature until slightly softened, about 10 minutes. On a lightly floured surface, roll out dough to just under 1/4 inch thick, adding more flour as needed to keep dough from sticking. Refrigerate until firm, about 30 minutes. Using a 3-inch bunny- or carrot-shaped cutter, cut out cookies; transfer to parchment-lined baking sheets. Reroll scraps once; cut out more shapes. Repeat with remaining disk. Freeze until very firm, about 15 minutes.

Bake, switching positions of sheets and rotating halfway through, until edges are light golden, 15 to 18 minutes. Transfer sheets to wire racks and let cool completely.

Transfer icing to a piping bag fitted with a small round tip (such as Ateco #3). Pipe a thin line of icing around the border of each cookie. Pipe an even layer of icing in center of cookies; using a toothpick, spread icing into corners and edges of cookies. Let stand at room temperature until set, at least 2 hours.

Place 1/4 teaspoon of each luster dust color in separate small bowls. Add 1 teaspoon water to each bowl and stir to combine. Working with one color at a time, use a small food-safe paintbrush to paint brushstrokes over surface of cookies, applying pressure to paintbrush to create more saturation. Let stand until dry, about 1 hour.