For the cookies: Put the sugar in a food processor and pulse a few times to finely grind. Add the flour, baking powder and salt and pulse just to combine.
Add the butter and pulse until all of the butter is incorporated into the flour and the mixture is sandy. Add the egg and vanilla and pulse until the mixture comes together in big clumps.
Turn the dough out onto a clean work surface and knead a few times to form a ball. Divide the dough in half, pat into 2 discs about 1/4 inch thick, wrap in plastic wrap and refrigerate until firm, about 1 hour.
Position an oven rack in the middle of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper.
Let the dough sit at room temperature for a few minutes to make rolling easier. Put 1 disc of dough between 2 pieces of parchment paper and roll out the dough to 1/8 inch thick. Cut out with desired cookie cutters and arrange on one of the prepared baking sheets about 2 inches apart. Bake until the bottom of the cookies are golden brown, 10 to 12 minutes. Cool on the baking sheet until firm enough to transfer to a rack to cool completely. Repeat with the remaining dough. Gently gather any scraps into a ball and press into another disc. Chill the disc until firm enough to roll and cut out as many cookies as possible.
For the icing: Sift together the confectioners' sugar and the meringue powder in a large bowl and add 6 tablespoons water. Beat with an electric mixer on medium-high until the mixture is glossy and soft peaks form, 3 to 4 minutes. Add food coloring if using or divide into several batches and color with different shades of food coloring. Decorate cookies as desired. The cookies can be store in an airtight container at room temperature for up to 3 days.
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