Make the cookies: Whisk the flour, 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 3 minutes. Beat in the honey, egg and vanilla until smooth. Reduce the mixer speed to low; beat in the flour mixture until combined. Divide the dough in half and shape each piece into a disk; wrap each disk in plastic wrap. Refrigerate until firm, at least 4 hours or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Working with 1 disk at a time, flour the dough and roll out until 1/8 inch thick on a lightly floured surface. Cut into shapes with 3-inch cookie cutters. Arrange 1 inch apart on the prepared pans. Reroll the scraps and cut out more cookies. (If the dough is too soft to work with, refrigerate until firm.)
Bake, switching the pans halfway through, until the cookies are lightly browned, 18 to 20 minutes. Let cool on the pans.
Meanwhile, make the icing: Whisk the meringue powder and confectioners? sugar in a large bowl. Beat in 5 tablespoons water with a mixer on medium speed until soft glossy peaks form. Beat in up to 1 more tablespoon water to thin the consistency if necessary. Spread or pipe the icing onto the cookies.