01 - Whisk together flour, baking powder, and salt in a medium bowl. Set aside for later use.
02 - Beat butter and sugar in a large bowl until light and fluffy, approximately 2-3 minutes.
03 - Add egg and vanilla extract to the butter mixture, mixing until fully incorporated.
04 - Gradually add dry ingredients to the wet mixture, mixing just until incorporated. Do not overmix.
05 - Divide dough in half, shape into discs, wrap 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 out 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, spacing 1 inch apart.
09 - Bake for 9-11 minutes, until edges are just golden. Cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
10 - Mix powdered sugar, 2 tablespoons milk, corn syrup, and vanilla until smooth. Add more milk if needed for a thick but pourable consistency.
11 - Divide icing into two bowls. Tint one bowl deep blue, the other black. Swirl the two colors together gently in a shallow dish.
12 - Dip cooled cookies face-down into the marbled icing. Immediately sprinkle with edible stars. Let set for at least 30 minutes.