Beat sugar and shortening in large bowl at medium speed of electric mixer until well blended. Add eggs, corn syrup, vanilla, orange peel and anise seed. Beat until well blended and fluffy.
Combine 3 cups flour, baking powder, baking soda and salt in medium bowl. Add gradually to shortening mixture, beating at low speed until well blended. Wrap dough in plastic wrap. Refrigerate 1 hour or overnight.
Divide dough into 4 equal pieces. Shape each into a disk. Wrap with plastic wrap. Refrigerate 1 hour or until firm.
Heat oven to 375 degrees F. Sprinkle about 1 tablespoon flour on large sheet of wax paper. Place disk of dough on floured paper. Flatten slightly with hands. Turn dough over. Cover with another large sheet of wax paper. Roll dough to 1/4-inch thickness. Remove top sheet of wax paper. Cut out with 2-inch floured cookie cutter. Place 2-inches apart on ungreased baking sheet. Repeat with remaining dough.
Combine sugar and cinnamon. Brush cookies with milk. Sprinkle cookies with sugar mixture.
Bake 7 to 9 minutes or until cookies are lightly set. Cool 2 minutes on baking sheet. Remove cookies to rack to cool completely.