• Sift the flour into a large bowl, and set it aside. Separate the egg, place the egg yolk in a small bowl. Place the egg white in its own container and refrigerate until ready to use.
• Place the sugar in a small bowl. Lay the vanilla bean flat. Look for the rougher, matte side – this is where the bean naturally splits open and where you want to cut.
• Hold the tip of the bean down with your finger. Using the sharp tip of a paring knife, carefully cut lengthwise down the center of the bean, following the matte side. Don't cut all the way through! Leave the end intact so the bean unfolds like a book.
• Use the blunt back of the paring knife to gently scrape the fragrant vanilla bean seeds from the bean and into the small bowl with the sugar. Use your fingers to rub the vanilla seeds into the sugar until they are distributed throughout the sugar.
• Pour the vanilla-sugar mixture into the bowl of a stand mixer. Add the salted butter. Mix on medium speed until the sugar and butter look creamy, about 2 minutes.
• Add the egg yolk and mix on medium speed until the egg yolk is fully incorporated. Add all the flour and mix on medium-low speed just until the dough comes together into large pieces of dough.
• Turn out the dough onto a clean, lightly floured surface. Gently gather the dough into a disk by gently pressing it together and shaping it into a round disk. Divide the dough into two pieces, weighing about 350 grams each.
• Shape each dough half into a 7-inch long by 1-1/2-inch diameter log, by forming it into a short cylinder and then rolling it back and forth with open hands. Move your hands from the center to the outside edges and back again to maintain even thickness. Add additional flour to the surface as needed to keep the dough from sticking.
• Wrap wax paper around the dough log, lengthwise. Then twist each end of the paper into pigtails in opposite directions (one towards you and one away from you) to form a locking mechanism. With each twist, the dough will compress and become smoothed out (think of it like a sausage in a casing). Roll from the center outward until you feel that you have a smooth, cylindrical log.
• Chill the dough for at least 1 hours and up to 2 days.

Baking the Cookies

• Preheat the oven to 325°F degrees. Remove one of the cookie dough logs from the refrigerator and let it sit at room temperature for 10 minutes. Brush the entire cookie dough log with egg white and sprinkle the dough with turbinado sugar (or raw cane sugar). Press the sugar into the dough as you rotate the log.
• Slice the log with a sharp knife into 1/2-inch rounds and place them on a cookie sheet about 2-inches apart. If using the flaky sea salt, sprinkle a few flakes on the top of each cookie.
• Bake the cookies for about 15-17 minutes. The bottom of the cookie will be light golden brown. If the cookies are brown on top reduce the baking time by 1-2 minutes.
• Remove the cookies from the oven and let them cool on the cookie sheet for 5 minutes then use a spatula to move them to a wire rack.

Storage

• Store the cookies in airtight container for up to 2 weeks. The cookies taste even better on the second day.