Put the Granulated Sugar (1/3 cup) and seeds from the Vanilla Bean Pod (1) in the bowl of a stand mixer or in a large bowl in which you can use a hand mixer. Using your fingertips, rub the vanilla into the sugar until it’s fragrant.
Add the Unsalted Butter (1 cup), the Powdered Confectioners Sugar (1/3 cup) and Fine Sea Salt (1/2 teaspoon) to the bowl. Using the paddle attachment, beat on low speed until the mixture is smooth and creamy (you don’t want it to get light and fluffy), scraping down the sides and bottom of the bowl as needed.
Drop in yolk of the Egg (1) and beat for one minute. Add the All-Purpose Flour (2 cup) all at once. Mix on low speed just until the flour has disappeared.
Turn the dough out onto a work surface and divide it in half. Shape each half into a log about nine inches long. Wrap the logs in parchment or plastic film and refrigerate for at least three hours.
When you’re ready to bake, preheat the oven to 325 degrees F (160 degrees C). Line a baking sheet with parchment paper or a silicone baking mat. Add a splash of cold water to the Egg White and mix with a fork to blend. Brush each log with this egg wash and roll it in Sanding Sugar (to taste) until it’s evenly coated.
Using a sturdy knife, trim the ends of the logs if they’re ragged, then cut the dough into half-inch-thick rounds. Place as many cookies as will fit on the baking sheet, spacing them about two inches apart.
Bake cookies for 18 to 22 minutes, rotating the pan halfway. The cookies are baked when they are brown around the edges and golden on the bottom. Let cool briefly on sheet pan, then carefully transfer them to a cooling rack and cool to room temperature. Repeat the baking with the remaining dough.