01 - In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
02 - In a large bowl, beat butter and sugar until light and fluffy, about 2-3 minutes.
03 - Add the egg and vanilla extract, mixing until combined.
04 - Gradually add the dry ingredients, mixing just until incorporated.
05 - Divide dough in half, shape into discs, wrap in plastic wrap, and chill 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. 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.
09 - In a bowl, mix powdered sugar, 2 tablespoons milk, corn syrup, and vanilla until smooth. Add more milk if needed for a thick but pourable consistency.
10 - Divide icing into two bowls. Tint one bowl deep blue, the other black. Swirl the two colors together gently in a shallow dish.
11 - Dip cooled cookies face-down into the marbled icing. Immediately sprinkle with edible stars. Let set for at least 30 minutes.