Using a spice/coffee grinder, ground the natural cane sugar in 3 batches until it is fine and powdery. Set aside.

Reserve 30 of the whole pecan-halves to use as garnishing. It should be ½ cup in total.

Whisk together egg yolks, water, vanilla extract, and butter in a small mixing bowl until combined. Set aside.

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.

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.

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.

Using a knife, divide the dough into two equal pieces.

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.

When ready to bake, pre-heat the oven to 325 F degrees. Line two baking sheets with parchment paper.

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.

Brush cookies with the egg white-water mixture, then gently press the reserved pecan halves into center of each cookie.

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.