Step 1

Preheat the oven to 350°F and set an oven rack in the middle position.

Step 2

Place the pecans on a baking sheet and toast for around five minutes, until fragrant. Cool on the baking sheet. (The nuts can be toasted and stored at room temperature.)

Step 3

In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, confectioners' sugar, vanilla, and salt until smooth and lightened a bit, two to three minutes. Scrape the bowl with a spatula. Add the flour and mix on low just until fully combined. Add the pecans and mix until evenly combined.

Step 4

Turn the dough onto a clean countertop lightly dusted with flour. Dust the dough with a little flour. Shape and roll into a squared log between 1-1/2 to 2 inches wide and 1-1/2 to 2 inches high, dusting with more flour as necessary. Wrap the dough in plastic wrap or parchment paper and chill for at least one hour or overnight, until the dough has gotten very firm.

Step 5

Preheat the oven to 350°F and set two oven racks in the centermost positions. Line two baking sheets with parchment paper.

Step 6

Lightly beat the egg yolk and 1/2 teaspoon of water in a small bowl and set aside. Pour the demerara sugar into a rimmed baking sheet or shallow casserole pan. Slice the chilled log in half to make it more manageable. Working with one log at a time, brush all sides of the log with the egg yolk mixture, then roll in the demerara sugar, pressing as necessary, until fully coated. If there are any areas of the log that are bare, sprinkle with the demerara sugar to cover.

Step 7

Use a serrated knife to slice each log into about 12 individual cookies, each about 1/2-inch thick. Place the cookie slices onto the prepared baking sheets, leaving about 2 inches of space between each. Bake, rotating from top to bottom and front to back halfway through, until lightly golden, 18 to 20 minutes. Let the cookies cool on the baking sheets for a few minutes, then transfer to a rack to cool completely. The cookies will keep in a covered container at room temperature for up to a week.

Step 8

Freezer-Friendly Instructions: Let the cookies cool completely and store in an airtight container separating layers with parchment paper or aluminum foil. Before serving, remove the cookies from the container and let them come to room temperature. If you'd like to freeze the dough before baking, shape it into a squared log, then wrap it securely in plastic wrap and then a layer of foil; freeze for up to 3 months. When ready to bake, remove the log from the freezer, thaw it until pliable, and then proceed with recipe.