In a large bowl, cream together the softened unsalted butter and granulated sugar using an electric mixer until light and fluffy, about 2-3 minutes. This process incorporates air, which is key to the cookies' texture.

Beat in the egg yolk and vanilla extract until well combined. Scrape down the sides of the bowl as needed to ensure everything is incorporated evenly.

In a separate medium bowl, whisk together the all-purpose flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix, as this can lead to tough cookies.

The dough will be soft. You can either chill the dough in the refrigerator for about 30 minutes to make it easier to handle, or proceed directly to shaping.

Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.

On a lightly floured surface, gently roll out the dough to about 1/4-inch thickness. Use your favorite cookie cutters to cut out shapes. Reroll scraps gently, chilling if necessary, to cut more cookies.

Carefully place the cut-out cookies onto the prepared baking sheets, spacing them about 1 inch apart.

Bake for 9-12 minutes, or until the edges are lightly golden brown. The centers should still look slightly soft. Baking time will vary depending on the size and thickness of your cookies.

Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. This allows them to set properly.