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

Combine butter and sugar in a large bowl; beat with an electric mixer until smooth and creamy. Add egg and beat until light and fluffy. Mix in corn syrup and orange peel until well combined.

Sift together flour, cinnamon, ginger, cloves, and salt in a separate bowl; stir into creamed butter mixture until blended. Shape dough into several balls, wrap in plastic wrap, and place in the refrigerator until thoroughly chilled, at least 1 hour.

Working in batches, place one ball of chilled dough on a floured surface and roll to 1/4-inch thickness. Cut out cookies with desired cookie cutters and place on ungreased cookie sheets. Repeat with remaining dough.

Bake in the preheated oven until edges are firm, 8 to 10 minutes. Cool on the baking sheet for 1 minute before removing to a wire rack to cool completely.