Preheat your oven to 325°F (165°C) and line two baking sheets with parchment paper.
In a large mixing bowl, cream together the softened butter and powdered sugar using an electric mixer on medium speed for 2-3 minutes until light and fluffy.
Add the vanilla extract and mix until combined.
In a separate bowl, whisk together the flour and salt. Gradually add the flour mixture to the butter mixture, mixing on low speed until just combined. Don't overmix—the dough should just come together.
Turn the dough out onto a lightly floured surface and roll to 1/4-inch thickness. Cut into desired shapes using cookie cutters or cut into traditional rectangles or wedges.
Place cookies on prepared baking sheets about 1 inch apart. Prick each cookie several times with a fork for that classic shortbread look, and sprinkle with granulated sugar if desired.
Bake for 18-20 minutes until the edges are just barely golden. The tops should remain pale.
Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Store in an airtight container for up to 2 weeks.