Remove dough from refrigerator. Transfer to a clean, lightly floured surface and use a rolling pin to roll dough to be between ¼-½” (about 1 cm) thick.
Use a 2” (5cm) round cookie cutter to cut out cookies as close together as possible and place on prepared baking sheet, spacing cookies at least 2” (5cm) apart.
Bake in 350F (175C) oven for 8-10 minutes. Allow cookies to cool on baking sheet for at least 5-10 minutes before carefully removing to cooling rack to cool completely.
Add about half the powdered sugar, corn syrup, vanilla extract, and salt and stir until smooth and thoroughly combined, then slowly stir in remaining powdered sugar.