In a large mixing bowl, cream together the butter and granulated sugar until light and fluffy, about 3-4 minutes.

Add in the egg and vanilla extract, mixing well until fully incorporated.

In a separate bowl, whisk together the flour and salt. Gradually add these to the butter-sugar mixture, mixing just until combined.

Divide the dough into two equal portions and roll each into a log shape, tightly wrapping in plastic wrap.

Refrigerate for at least 4 hours or overnight.

Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.

Remove logs from the refrigerator, slice into ¼-inch thick rounds, and place on the prepared baking sheet.

Bake for 10-12 minutes, or until the edges are lightly golden.

Let cookies cool on the baking sheet for about 5 minutes before transferring to wire racks.