Whisk the flour, cornmeal, baking powder, and salt in a medium bowl. In another bowl, beat the butter with a handheld electric mixer until smooth.
Add the sugar, vanilla, and anise to the butter and continue beating until light and fluffy, about 2 minutes more.
Add the eggs 1 at a time to the butter mixture and mix until incorporated, about 30 seconds. Stir the flour-cornmeal mixture into the wet ingredients with a wooden spoon or rubber spatula.
Divide the dough into 34 (1-inch) balls (3/4-ounce). Arrange the cookies on 2 parchment-lined cookie sheets about 1-inch apart. Make a hole in the center of each ball with your finger or the tip of a wooden spoon. Work each piece of dough by hand into a doughnut-like shape with a 1-inch hole and about 2 inches wide. Use scissors to snip 1/2-inch long angled cuts, about 1/2-inch apart around the outside ring of each cookie. Freeze cookies on the sheet until firm, about 10 minutes.
Preheat oven to 350 degrees F.
Toss a few of the cornflakes at a time with the egg whites and arrange on the surface of the cookies in a leaf like pattern.
Bake until just golden around the edges, about 14 to 18 minutes.
Transfer to a rack to cool. Dust with confectioners' sugar.
