Preheat the oven to 375 degrees F (190 degrees C).

Beat sugar and shortening on medium speed with an electric mixer in a bowl until well blended. Add eggs, corn syrup, and vanilla; beat well. Combine flour, baking powder, baking soda, and salt in a separate bowl. Gradually add flour mixture to egg mixture on low speed until well blended.

Wrap dough in plastic wrap and chill in the refrigerator for 1 hour.

Roll out dough between 2 sheets of lightly floured wax paper. Cut out desired shapes with a floured cutter and place them on ungreased cookie sheets.

Bake cookies in the preheated oven until the centers are set, 6 to 10 minutes. Baking time will depend on the size and thickness of cookies; do not overbake. Cool briefly, then remove from the cookie sheets to cool to room temperature.