Preheat the oven to 350°F and place the pecans on a baking sheet. Toast for about 5 minutes until fragrant, then cool.

In the bowl of an electric mixer fitted with the paddle attachment, cream together the butter, confectioners' sugar, vanilla extract, and salt until smooth and slightly lightened, about 2–3 minutes.

Add the flour and mix on low speed until just combined, then stir in the toasted pecans.

Turn the dough onto a lightly floured surface and shape it into a squared log about 1½ to 2 inches wide and high. Dust with a little flour as needed.

Wrap the dough in plastic wrap or parchment paper and chill for at least 1 hour or overnight until firm.

Preheat the oven to 350°F and line baking sheets with parchment paper.

Beat the egg yolk with ½ tablespoon of water. Pour the demerara sugar into a shallow dish.

Slice the chilled log in half. Brush all sides with the egg yolk mixture, then roll in the demerara sugar to coat.

Use a serrated knife to slice the log into about 12 cookies per half, each about ½ inch thick. Place cookies on the prepared sheets about 2 inches apart.

Bake until lightly golden, rotating the sheets halfway through, about 18–20 minutes. Cool on the baking sheets before transferring to a rack to cool completely.