Add the butter and sugar to a large bowl or the bowl of a stand mixer, and use an electric mixer on medium speed or the stand mixer fitted with the paddle attachment to cream the mixture until light and fluffy, about 3 minutes, scraping down the bowl halfway.

Scrape down the bowl, then beat in sourdough discard and vanilla extract on medium low speed until combined.

Scrape down the bowl again, then on low speed beat in the flour and salt until combined.

Scoop out half the dough (about 335 grams) onto a piece of plastic wrap, waxed paper, or parchment paper. Using the wrap or paper to help you, roll the dough into a log about 1 ½ inches wide. Repeat with the other half of the dough.

Chill the logs for at least 4 hours, but you can leave them for up to 24 hours.

When ready to bake, preheat the oven to 350ºF with racks in the upper and lower third. Line two sheet pans with parchment paper.

Pour the Demerara sugar, cinnamon, and flaky salt into a shallow dish or another sheet pan and use your fingers to combine.

Unwrap one cookie log. Brush it lightly with the beaten egg white, then roll in the sugar mixture, pressing firmly so it adheres to the dough.

Slice into ¼-inch-thick rounds. Lay cookies out on the parchment about 1 inch apart from each other.

Bake until puffed and lightly golden brown, 14 to 16 minutes, swapping the tray racks halfway through baking.

Let cool completely, then store in an airtight container for up to one week (or freeze for up to 3 months).