Pecan Shortbread Cookies

Preheat the oven to 350 degrees F. Spread the chopped pecans on a rimmed baking sheet and toast for about 6 minutes, until lightly browned and fragrant. Let cool. In the bowl of a standing mixer fitted with the paddle, beat the butter with the confectioners' sugar, vanilla bean and seeds, vanilla extract, and salt at medium speed until fluffy, about 3 minutes. Add the flour in 3 batches, beating at low speed until just incorporated. Discard the vanilla bean. Stir in the pecans. Transfer the dough to a work surface and roll into a 1 1/2-inch-thick log. Wrap the log in plastic or parchment paper and refrigerate for about 1 hour, until chilled. Line 2 large rimmed baking sheets with parchment paper. Spread the demerara sugar on a platter. Brush the log with the egg yolk and roll in the sugar. Slice the log into 1/2-inch-thick rounds. Transfer the rounds to the prepared baking sheets, spacing them 1 inch apart. Bake the shortbread cookies for about 20 minutes, until the edges are golden; rotate the baking sheets from top to bottom and front to back halfway through baking. Transfer the cookies to a wire rack and let stand until cooled completely, about 30 minutes, before serving.