Beat the butter at medium speed until smooth and very creamy. Add the sugars and salt and beat until well blended, about 1 minute. The mixture should be smooth and velvety, not fluffy and airy. Reduce the mixer speed to low and beat in 2 of the egg yolks, again beating until the mixture is homogeneous.
Turn off the mixer. Pour in the flour, drape a kitchen towel over the stand mixer to protect yourself and the counter from flying flour and pulse the mixer at low speed about 5 times, a second or two each time. Take a peek -- if there is still a lot of flour on the surface of the dough, pulse a couple more times; if not, remove the towel. Continuing at low speed, mix for about 30 seconds more, just until the flour disappears into the dough and the dough looks uniformly moist. (If most of the flour is incorporated but you've still got some in the bottom of the bowl, use a rubber spatula to work the rest of the flour into the dough.) The dough will not clean the sides of the bowl, nor will it come together in a ball -- and it shouldn't. You want to work the dough as little as possible. What you're aiming for is a soft, moist, clumpy (rather than smooth) dough. Pinch it, and it will feel a little like Play-Doh.
Scrape the dough out onto a smooth work surface, gather it into a ball and divide it in half. Shape each piece into a smooth log about 9 inches long: it's easiest to work on a piece of plastic wrap and use the plastic to help form the log. Wrap the logs well and refrigerate them for at least 3 hours, preferably longer.
GETTING READY TO BAKE: Center a rack in the oven and preheat the oven to 350 degrees F. Line two baking sheets with parchment or silicone mats.
Remove a log of dough from the refrigerator, unwrap it and place it on a piece of parchment or wax paper. Whisk the remaining egg yolk until it is smooth, and brush some of the yolk all over the sides of the dough -- this is the glue -- then sprinkle the entire surface of the log with decorating sugar.
Trim the ends of the roll if they're ragged, and slice the log into 1/3-inch-thick cookies. Place the rounds on the baking sheets, leaving an inch of space between them.
Bake one sheet at a time for 17 to 20 minutes, rotating the baking sheet at the midway point. When properly baked, the cookies will be light brown on the bottom, lightly golden around the edges and pale on top; they may feel tender when you touch the top gently, and that's fine. Remove from the oven and let the cookies rest a minute or two before carefully lifting them onto a rack with a wide metal spatula to cool to room temperature.
Repeat with the remaining log of dough, making sure the baking sheets are cool before you bake the second batch.
Mix just until the flour disappears into the dough and the dough looks uniformly moist.
If most of the flour is incorporated but you've still got some in the bottom of the bowl, use a rubber spatula to work the rest of the flour into the dough.
The dough will not clean the sides of the bowl, nor will it come together in a ball -- and it shouldn't. You want to work the dough as little as possible.
Pinch it, and it will feel a little like Play-Doh.