Whisk flour, baking powder, and salt. Beat butter and sugar until fluffy, then beat in egg and vanilla. Gradually add dry ingredients. Shape dough into two discs, wrap, and refrigerate for at least 2 hours.

Preheat oven to 350°F (175°C). Roll one disc of dough to 1/4-inch thickness between floured parchment. Cut 3-inch circles and place on parchment-lined baking sheets.

Bake 10 to 12 minutes, until edges are just golden. Cool on the sheets 5 minutes, then transfer to a rack to cool completely.

Beat powdered sugar, meringue powder, and 3 tablespoons water on high for 4 minutes until stiff peaks form. Divide icing; tint half with red gel coloring. Adjust consistency with water or powdered sugar as needed.

Pipe white icing circle on each cookie, smooth with a toothpick, let set 20 minutes. Pipe red curved seams and stitches. Dry uncovered at least 2 hours before stacking.