Make the cookies: Sift the flour, baking powder and salt into 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 vanilla and beat until combined. Reduce the mixer speed to medium low and beat in the flour mixture in 2 batches until just combined. Divide the dough between 2 large pieces of plastic wrap. Flatten into disks and wrap. Refrigerate until firm, at least 4 hours or overnight.
Line 2 baking sheets with parchment paper. Roll out 1 disk of dough on a lightly floured surface until about 1/8 inch thick, dusting with more flour as needed. Cut out sweaters using a 3- to 3 1/2-inch cutter. Gather the scraps, reroll and cut out more cookies. (If the dough becomes too soft, refrigerate 15 minutes.) Arrange the cutouts 1 inch apart on the prepared pans. Refrigerate until firm, about 30 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350˚. Bake the cookies, switching the pans halfway through, until lightly browned around the edges, 15 to 18 minutes. Let cool 5 minutes on the pans, then remove the cookies to racks to cool completely.
Meanwhile, make the icing: Whisk the confectioners' sugar and meringue powder in a large bowl. Beat in 5 tablespoons water with a mixer on medium-high speed until soft, glossy peaks form, adding the remaining tablespoon water if needed. You’ll need 2 consistencies of icing: a thicker icing for outlining and a thinner, runnier icing for filling (flooding). Adjust the consistency with water as needed. Tint with food coloring, if desired. Transfer to resealable plastic bags, snip the corners and decorate the cookies. Sprinkle with coconut, if desired. Let set, at least 1 hour.