Make the cookies: Sift together the flour, ginger, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 5 minutes. Add the egg and beat until combined. Reduce the mixer speed to low; add the flour mixture in 2 batches and beat until just incorporated. Divide the dough between 2 sheets of plastic wrap; shape each into a disk. Wrap and refrigerate until firm, at least 4 hours.
Line 2 baking sheets with parchment paper. Working with 1 piece at a time, lightly flour the dough and roll out until 1/8 inch thick. Cut out shapes with a 3-inch cookie cutter and arrange 1 inch apart on the baking sheets. Refrigerate the cutouts 30 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Bake, switching the pans halfway through, until the cookies are light golden around the edges, 15 to 18 minutes. Let cool 5 minutes on the baking sheets; transfer to racks to cool completely.
Make the icing: Whisk the confectioners¿ sugar and meringue powder in a large bowl. Add 5 tablespoons water; beat with a mixer on medium-high speed until soft peaks form, adding up to 1 more tablespoon water as needed. Tint with food coloring, if desired. Spread or pipe on the cookies. Sprinkle with nonpareils. Let set, about 1 hour.