Beat the sugar and eggs with an electric mixer until pale and creamy (1-2 minutes). Add the butter and beat until thoroughly mixed and creamy.
Whisk the corn and all-purpose flour together. Add them to the sugar mixture. Beat on low just until blended. Do not overbeat.
Lightly flour a working surface. Turn the dough onto the surface and pat it to flatten. Divide the dough in half and form two discs. Wrap each disc in plastic wrap. Refrigerate the discs for 30 minutes.
Lightly flour a work surface and rub flour on the rolling pin. Unwrap one disc and roll it to 1/4-inch thick. Then cut out 2-inch round circles with a cookie cutter. Reshape leftover dough and cut cookies until it is used. Do not overwork the dough when reshaping and rolling it out. Place the cookies on the prepared baking sheet 1/2 inch apart. Refrigerate for 30 minutes to chill the dough again. Repeat for the other chilled cookie disc.
While the cookies chill, preheat the oven to 350°F. Bake for 17-19 minutes until the cookies are lightly browned around the edges. Rotate the cookie sheet after 9 minutes. If baking two sheets at a time, rotate them from the top to the bottom rack and turn pans around to help all the cookies bake evenly.
Remove from the oven and let the cookies cool for a couple of minutes. Then place them on a wire rack to cool completely. Store in an airtight container for up to a week or in the freezer for a month.
Notes
Freezing the Dough
You can make the dough ahead of time and store it in the freezer for up to three months if wrapped well and kept in an airtight container. Thaw overnight or for 3 hours at room temperature before rolling.