In the bowl of a food processor fitted with an S-shaped blade (the standard blade), pulse together the butter and granulated sugar until combined, scraping down the sides of the bowl with a spatula as needed.
Zest the lemons into the small bowl containing two egg yolks, then add in the pinch of salt, vanilla extract, and the 1 tbsp lemon juice. Whisk together with a fork until just combined.
Add the liquid mixture to the butter and sugar in the food processor and pulse until mixture is smooth and creamy. Scrape down the sides of the bowl as needed.
Add 1 cup of flour to the food processor and pulse until flour is just combined. Scrape down sides of bowl, then add the 2ndcup of flour and pulse until all flour is just incorporated and you have a soft dough. Do not overmix.
Carefully scrape the sable cookie dough onto the plastic wrap. Pat dough into a square, wrap well, and freeze for 10 minutes, or until dough is chilled and a little firm.
Sprinkle powdered sugar onto your work surface and unwrap chilled dough. Use a rolling pin to roll the dough out to 1/8-inch thickness; you may need to roll the dough out in batches, and don’t worry if it cracks at the edges.
Use a cookie cutter to cut out your desired sable cookie shapes. Place cookies on the prepared cookie sheets; you can fit 9-12 cookies on each sheet since they won’t spread in the oven. Gather dough scraps and repeat rolling andcutting process as needed.
Chill the sable cookies on the cookie sheets in the fridge for 10-15 minutes.
Remove cookie sheets from the fridge and immediately brush with the egg yolk and water mixture, then sprinkle lightly with Turbinado sugar.
Bake sable cookies at 325F until light golden brown, 12-14 minutes.
Remove sable cookies from oven and cool on sheets for 2-3 minutes, then transfer cookies to a wire rack to cool completely.