In the bowl of a mixer fitted with the paddle attachment, combine butter, vanilla bean seeds scraped from the vanilla bean pods, and sugar. Beat on medium-high until light and fluffy, about 2-3 minutes. Add the egg yolks one at time and the vanilla, mixing after each addition. Turn the mixer to low, and slowly add the flour and salt, mixing until fully incorporated.
Turn the dough out onto a piece of parchment paper. Using your hands, roll the dough into a log about 1½-1¾ inches in diameter. Wrap the parchment paper tightly around the log, twisting the ends inward to seal. Place the log in the freezer and chill until very firm (2-3 hours).
When you are ready to slice and bake, remove cookie dough from the freezer and let it sit at room temperature for about 10 minutes. Position oven racks in the top and bottom thirds of the oven, and preheat the oven to 350˚F. Line two baking sheets with parchment paper or silicone baking mats. Using a fork, whisk the egg white and water. Sprinkle about 1/2 cup turbinado sugar on the parchment paper along the side of the dough log, but not touching. Brush the dough lightly with the egg wash, then roll the log in the sugar until all sides are coated. Using a sharp knife, slice each cookie into rounds about ⅜-inches thick. Place the sliced cookies on the prepared baking sheets, leaving at least 1-inch between each round.
Bake the cookies, rotating and swapping the baking sheets halfway through, until the cookies begin to brown around the edges and are completely set. 14-16 minutes total. Let cool on the sheets for 5 minutes, then carefully transfer to a wire rack until they cool completely. (These are not the kind of cookie to eat warm... make sure to let them cool and so that the texture sets). Store cookies in an airtight container for up to 1 week.
*Vanilla and vanilla beans at the grocery store are so expensive. Costco has the best in-store price I've come across, though I recommend ordering vanilla beans online - you can get 10 for the price of 2 at the store. Just do a little research and read reviews first. Use Grade A when you use the seeds in a recipe, Grade B for making extracts. Also, I came across vanilla bean powder a few years ago when I did the Whole30. I use it in a pinch when something calls for vanilla beans and I don't have any on hand. It is less flavorful since it is the whole bean ground into a powder, not just the seeds.
** To make vanilla sugar, slice vanilla beans lengthwise and scrape out the seeds for later use. Add the empty pods to an airtight container with sugar for at least two days (or an indefinite period of time). If you're making these cookies right now and don't have a few days, regular sugar works just fine. This last time I baked these cookies, I forgot about the vanilla sugar. Guess what? They were still delicious.
***When baking with gluten-free all-purpose flour, I prefer to use Bob's Red Mill 1-to-1 Baking Flour. I get much better results with that than King Arthur's GF flour or any others I have tried.
Source: Everyday Annie