In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2–3 minutes using a hand mixer or stand mixer.

Mix in the egg yolks and vanilla extract until fully incorporated and smooth.

Stir in the salt and flour, mixing just until a dough forms. Do not overmix. The dough will be soft but should hold together well.

Divide the dough in half and shape into logs or disks. Wrap in plastic wrap and chill in the refrigerator for at least 1 hour to firm up.

Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. If using log-shaped dough, slice into ¼-inch thick rounds. For disk-shaped dough, roll out to ¼-inch thick and cut with a round cookie cutter.

Place cookies on the prepared sheet. Whisk the egg yolk with water and brush over each cookie. Use a fork to create a crisscross pattern or decorative lines. Sprinkle with coarse sugar if desired.

Bake for 12–15 minutes or until the edges are lightly golden. Let cool on the baking sheet for a few minutes before transferring to a wire rack.