Naturally Sweetened Pecan Shortbread Cookies

1 Using a spice/coffee grinder, ground the natural cane sugar in 3 batches until it is fine and powdery. Set aside.
2 Reserve 30 of the whole pecan-halves to use as garnishing. It should be ½ cup in total.
3 Whisk together egg yolks, water, vanilla extract, and butter in a small mixing bowl until combined. Set aside.
4 Place the rest of the pecans (approximately ½ cup) in the bowl of a food processor and process until coarsely ground. Add in the flour, cinnamon, salt, and nutmeg. Process until combined.
5 While the food processor is still running, add the butter mixture through the tube. Process until thoroughly combined. You may have to stop the food processor a few times and scrape the bottom of the bowl with a spatula.
6 Transfer the dough onto a clean work surface and knead until smooth. It might be a little powdery, but it will come together as you knead with the body heat from your hands.
7 Using a knife, divide the dough into two equal pieces.
8 Roll each dough into a 6-inch log that is about 2-inches thick. Wrap each log tightly using stretch film and place upright in tall glasses. Refrigerate until firm, at least 2 hours up to 2 days.
9 When ready to bake, pre-heat the oven to 325 F degrees. Line two baking sheets with parchment paper.
10 Working with one log of dough at a time, slice into ¼-inch thick cookies, turning log every few slices to prevent sides from flattening. Space them ¾-inch apart from each other on prepared sheets.
11 Brush cookies with the egg white-water mixture, then gently press the reserved pecan halves into center of each cookie.
12 Bake one sheet at a time, until the edges of cookies are beginning to brown and set, 16-19 minutes, rotating the sheet halfway through baking. Let the cool before serving.