Beat butter and sugar at medium speed in a stand mixer until light and fluffy, about 5 minutes.

In a separate bowl, beat egg whites at high speed until stiff peaks form. On low, beat egg whites into butter mixture, just until blended. Still on low, add egg yolk, 1 and 1/2 tablespoons orange zest, 2 tablespoons orange juice and vanilla to butter/egg white mixture, beating just until blended. In a separate bowl, lightly whisk together the flour, cornmeal, baking powder, and salt. Add to butter mixture in three parts, beating just until blended after each addition.

Divide the dough in half, and wrap each half in plastic wrap. Flatten dough into discs and refrigerate for 8 hours or freeze for 1/2 hour. Dough is very soft and must be chilled before handling.

Preheat oven to 350 degrees. Roll out one portion of dough on a floured surface with a floured rolling pin to 1/4 inch thickness. Cut into shapes with floured cookie cutters and place cut outs on parchment lined cookie sheets (or roll dough directly onto parchment paper, cut out cookies and remove trimmings. Place parchment paper onto cookie sheet and bake). Re-roll trimmings for additional cookies. Keep dough refrigerated between rollings.

Bake for about 10 to 11 minutes or until just starting to brown. Cool cookies on cookie sheet for 5 minutes, then remove cookies to wire racks until completely cooled.

For orange glaze/frosting, combine remaining 1/2 tablespoon zest, remaining 3 tablespoons orange juice, and powdered sugar in a medium bowl, whisking until smooth. (Add a little more sugar to make the frosting thicker, if you like, or add a few drops of orange juice if you'd like it to be thinner). Spread topping on stars. Place cookies on wire racks until topping is set, about half an hour or so, depending on how thick it is.