Preheat your oven to 325°F (165°C). Lightly grease the bottom and sides of a 10-inch cast iron skillet with a thin layer of butter.
In the bowl of a stand mixer, or using a large bowl with a hand mixer, beat the softened unsalted butter and powdered sugar on medium speed for 3 minutes until light, pale, and very fluffy.
Beat in the vanilla extract until fully incorporated.
Turn the mixer to its lowest speed setting. Gradually add the all-purpose flour and salt. Mix just until the dough comes together into crumbly clumps. Do not overmix!
Dump the crumbly dough directly into the prepared cast iron skillet. Use your hands to press it firmly and evenly across the bottom, reaching all the edges.
Use a fork to prick a decorative pattern of holes all over the surface of the dough. (This prevents the shortbread from bubbling up in the oven).
Using a sharp paring knife, score the raw dough into 12 even wedges, cutting only halfway down through the dough.
Bake in the preheated oven for 30-35 minutes, or until the edges touching the pan are a deep golden brown and the center is pale gold.
Remove the skillet from the oven. While the shortbread is still piping hot, use a sharp knife to cut all the way through the scored lines to the bottom of the pan.
Immediately sprinkle the 1 tablespoon of granulated sugar evenly over the hot surface.
Allow the shortbread to cool completely to room temperature inside the skillet before using a thin spatula to remove the wedges.