Preheat oven to 350°F. Line two baking sheets with parchment.
Cream butter and sugar in a bowl until pale and fluffy, about 2 minutes.
Beat in vanilla, orange zest, and milk until smooth.
Whisk flour, cornmeal, baking powder, and salt. Add to the bowl and mix just until a soft dough forms.
Dust the counter lightly with flour. Roll dough to about 1/4 inch thick.
Cut stars with a 2-inch cutter. Gather scraps and re-roll once to use up dough.
Bake 10–12 minutes until edges look set and lightly golden. Rotate pans halfway if needed.
Cool on the sheet 5 minutes, then transfer cookies to a rack to cool completely.
Whisk confectioners' sugar, orange juice, and orange zest until glossy and drizzleable.
Drizzle or dip cooled cookies in the glaze. Let set until the glaze firms.
Notes
Variation: Add 1/4 tsp almond extract to the dough for a bakery-style aroma, or swap lemon for orange in the glaze. Storage: Keep in an airtight container at room temperature up to 5 days, or freeze unglazed cookies for 1 month and glaze after thawing.This recipe is an original creation inspired by classic Cornmeal Stars with Orange Glaze flavors. All ingredient ratios and instructions are independently developed.