In medium-size bowl with electric mixer on medium speed, beat the butter and granulated sugar until light and fluffy. Beat in the egg, corn syrup, and vanilla extract until well mixed. Reduce speed to low and gradually beat in flour and salt. Divide dough into thirds and gather dough into balls. Flatten each ball into a 4-inch disk and wrap in plastic. Refrigerate disks at least 30 minutes or overnight.
Heat oven to 325 degrees F and lightly grease 2 baking sheets. Take out the dough of the plastic wrap and spray a little of pan spray on your hands (so the dough dont stick on your hands). Make little balls, squeeze them a little to give them the cookie shape and with a fork make a mark on top. Place cookies, spaced at least 1/2 inch apart, on baking sheet. Bake cookies until edges are lightly browned, 12 to 14 minutes. Cool cookies 5 minutes on baking sheet; transfer to wire rack and cool completely.