Cream the butter, sugar, and vanilla extract in a stand mixer fitted with a paddle attachment until it is light and fluffy, about 8-10 minutes.
Scrape down the sides of the bowl. Slowly add the flour, followed by the chopped pecans. Continue mixing just until the dough comes together.
Transfer the dough onto a work surface and roll it into a 2 inch wide log. Compress the dough as much as possible then roll it up tightly in plastic wrap. Place the log in the refrigerator for at least two hours (leave it overnight if you can).
When you are ready to bake the cookies, pre-heat the oven to 350ºF. Pour about a half a cup of Demerara sugar onto a quarter sheet tray or plate. Brush the outside of the dough with a beaten egg, then roll it in the sugar. I cut the log in half to make this step a little more manageable. Be sure that the entire surface is coated in sugar. Use a sharp knife to cut the log into 1/2 inch slices. Arrange the rounds onto two parchment lined sheet trays. These cookies don’t spread out, but you want to leave a little room in between so they bake evenly. Sprinkle a little flaky salt over each cookie.
Bake for 15 minutes, rotating the trays half way through the bake. The edges will be slightly golden, but the tops shouldn’t take on any color. Let the cookies cool completely before enjoying. As they cool, the cookies will dry and reach the perfect crisp texture!