Preheat the oven to 350°F. Line with parchment or lightly grease two cookie sheets or half-sheet pans and set aside.
Cream the butter and sugar together until light and fluffy. Scrape the bowl. Add the egg yolks, salt, and vanilla. Beat until combined and fluffy. Scrape the bowl to make sure everything is mixed well.
Add the flour and cornmeal and mix gently until everything is fully combined. Let the dough stand for about 5 minutes; the cornmeal will absorb some of the moisture from the butter and egg. Meanwhile, fill a shallow bowl with a layer of sugar.
After 5 minutes, check the consistency of the dough. The dough should be soft but firm enough to hold together and shape with your hands. If it is spreading, add a little more flour (up to 1/4 cup, but probably not even that much) and combine.
Using a spoon or small cookie scoop, roll pieces of cookie dough into 1" balls. Roll them in sugar, and place them on a lined cookie sheet, leaving about 2" of space between each
Using the flat bottom of a clean glass or the palm of your hand, lightly press the cookies to form thick disks. TIP: I prefer using a glass because I find it makes a more even, flat shape.
Bake on the center rack for about 15 minutes, rotating half way. The cookies should be pale gold and lightly brown on the bottom. Let cool on the cookie sheets for a few minutes to set before transferring to a cooling rack to cool completely. These will keep in an airtight container for a week or a little longer, and freeze well.