Mix the Dough
In a large bowl, combine butter, powdered sugar, corn starch, and flour. Mix together until well combined and the mixture starts to come together.
Knead Lightly
Turn the dough out onto a clean surface and knead lightly just until smooth. Don't overwork the dough or the cookies will be tough.
Shape the Cookies
Divide the dough in half. Roll each half into a circle about 1/4 inch thick. Use a biscuit cutter to cut out rounds. Place cookies on a parchment-lined baking sheet.
Bake
Preheat oven to 350°F. Bake for 15 minutes or until golden around the edges. The cookies should be pale in the center and just beginning to turn golden.
Finish and Cool
Immediately after removing from the oven, sprinkle the warm cookies with coarse sugar. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.