01 - Whisk together flour, baking powder, and salt in a medium bowl. Set aside for later use.
02 - Beat butter and granulated sugar in a large bowl until light and fluffy, approximately 2-3 minutes.
03 - Add egg and vanilla extract to the butter mixture. Mix until fully combined.
04 - Gradually add the dry ingredients to the wet mixture, mixing just until incorporated. Avoid overmixing.
05 - Divide dough in half and shape into discs. Wrap tightly in plastic wrap and refrigerate for 30 minutes.
06 - Preheat oven to 350°F. Line baking sheets with parchment paper.
07 - On a lightly floured surface, roll one disc at a time to 1/4-inch thickness. Cut out stars or rounds with cookie cutters.
08 - Place cookies on prepared baking sheets, leaving 1 inch of space between each cookie.
09 - Bake for 9-11 minutes until edges are just golden. Allow to cool on baking sheet for 5 minutes, then transfer to wire rack to cool completely.
10 - Mix powdered sugar, 2 tablespoons milk, corn syrup, and vanilla extract until smooth. Add additional milk if needed to achieve thick but pourable consistency.
11 - Divide icing between two bowls. Tint one bowl deep blue, the other black. Gently swirl the two colors together in a shallow dish without fully mixing.
12 - Dip cooled cookies face-down into the marbled icing. Immediately sprinkle with edible stars. Allow icing to set for at least 30 minutes before serving.