01 - Whisk together flour, baking powder, and salt in a medium bowl until thoroughly combined. Set aside for later use.
02 - Beat butter and granulated sugar in a large bowl with electric mixer until light and fluffy, approximately 2-3 minutes.
03 - Add egg and vanilla extract to the butter mixture, mixing until fully incorporated and smooth.
04 - Gradually add dry ingredients to wet mixture, mixing just until dough forms. Avoid overmixing to prevent tough cookies.
05 - Divide dough in half, shape into flat discs, wrap tightly in plastic wrap, and refrigerate for 30 minutes until firm.
06 - Preheat oven to 350°F. Line baking sheets with parchment paper.
07 - Roll one dough disc at a time on lightly floured surface to 1/4-inch thickness. Cut shapes using star or round cookie cutters.
08 - Place cutouts on prepared baking sheets, spacing 1 inch apart to allow for slight spreading during baking.
09 - Bake for 9-11 minutes until edges are lightly golden. Cool on baking sheet for 5 minutes, then transfer to wire rack.
10 - Mix powdered sugar, 2 tablespoons milk, corn syrup, and vanilla in bowl until smooth. Add remaining milk if needed for thick but pourable consistency.
11 - Divide icing between two bowls. Tint one deep blue, the other black. Pour both colors into shallow dish and swirl gently without fully blending.
12 - Dip cooled cookies face-down into marbled icing. Immediately sprinkle with edible stars while wet. Let set for at least 30 minutes.