In a mixer bowl fitted with the paddle attachment, beat butter, powdered sugar, and salt on medium speed for 2 minutes until creamy. Add egg yolk and vanilla extract and beat for about 30 seconds until combined. Add flour and beat on low speed just until combined. Do not over mix the dough. If dough is too dry, add water, 1-2 teaspoons at a time. To check if the dough is done, take a piece of dough and press it between your thumbs – the dough should stick well together without feeling dry.
On a lightly floured surface, work the dough until it comes together, then divide in half. Shape each half of dough into a log that is 1.5 inches in diameter. Roll logs into demerara sugar (if the dough is too soft and hard to handle, do this after refrigeration). Wrap logs in plastic wrap and refrigerate or freeze for at least 1-2 hours until firm. Dough can be left in the refrigerator for up to 3 days or in the freezer for 2 months.
Preheat oven to 350F/180C. Line 2 pans with parchment paper.
Once the dough is cold enough, and use a sharp knife to slice the logs into 1/4 to 1/2-inch thick rounds. If the dough is too crumbly and breaks, leave it for a few minutes to soften and squeeze any broken bits back into each cookie.
Arrange cookies on prepared baking sheets, placing them 2 inches apart. Bake for 10-12 minutes or until slightly golden brown around the edges. When done, the cookies should appear soft and bright. Allow cookies to cool on a wire rack.
Store cookies at room temperature in an airtight container for up to 5 days or in the fridge for up to 2 weeks, bringing to room temperature before serving. Cookies can also be frozen for up to 2 months.