Beat butter and sugar until light and fluffy, about 2 to 3 minutes. Add egg and vanilla, then beat to combine. Whisk flour, baking powder, and salt; mix into butter mixture on low just until incorporated.

Shape dough into a disk, wrap in plastic, and refrigerate at least 30 minutes or up to 2 days.

Preheat oven to 350°F (175°C). Roll chilled dough to ¼‑inch thickness on a floured surface. Use a soccer ball cutter to cut shapes; place on parchment‑lined sheets 1 inch apart, chilling again if dough softens.

Bake one sheet at a time 8 to 10 minutes, until edges are set and tops are dry. Cool on sheet 2 minutes, then transfer to a wire rack to cool completely.

Whisk powdered sugar, lemon juice, and milk into a smooth icing. Spread white icing over cookies; let set 5 minutes. Tint remaining icing black, then pipe or paint pentagons onto each cookie. Let dry 15 minutes before serving.