Preheat the oven to 350 degrees. Lay 2 cups of pecans in a single layer on a baking sheet and toast for 8-12 minutes, stirring once mid-way through baking until fragrant and browned. Remove from the oven and cool to room temperature.
Place the toasted pecans, brown sugar and confectioners sugar in the bowl of a food processor and pulse until the nuts are finely ground. Add the flour and salt and process to combine.
Add the butter and process until the mixture resembles wet sand and the mixture begins to ride up the sides of the bowl. Add the egg yolk and process until combined.
Cut a 15" long piece of parchment paper and place on a work surface. Transfer half the dough to the plastic wrap and roll it into a log shape, about 2" in diameter. Roll up to seal in the parchment and twist the ends gently to seal. Repeat with the remaining dough. Place cookie dough logs in the refrigerator and chill for 2 hours (or overnight) until firm.
When the dough is chilled and you're ready to bake, preheat the oven to 325°.
Arrange the oven rack to the center of the oven and line a sheet pan with parchment paper or a silpat.
Whisk the egg white with 1 teaspoon of water until frothy. Set aside.
Chop the remaining ½cup of pecans finely. Set aside.
Working with 1 dough log at a time, remove from plastic wrap and use a sharp chef's knife to cut the dough into 3/8" slices, rotating the log as you go so that the log doesn't become misshapen, from the weight of the knife. Place rounds 1" apart on the cookie sheet.
Use a pastry brush to lightly swab each cookie with egg white to coat the top. Sprinkle the cookies with chopped pecans, a sprinkle of sugar and light sprinkle of sea salt.
Bake cookies for 10-15 minutes or until cookies are lightly browned and crisp.
Cool cookies for 3 minutes on a baking sheet before transferring them to a wire rack to cool completely. Store in an airtight container.