Line a 9x13-inch metal baking pan with parchment paper. Set aside.
In a large mixing bowl, mix together 1 cup granulated sugar and 2 tablespoons lemon zest to infuse the sugar.
Add the 2 cups salted butter to the sugar and cream for 2 minutes, scraping down the sides of the bowl about halfway through.
Add 1 teaspoon vanilla extract and mix until incorporated.
In a separate, large mixing bowl, whisk together 5 cups all-purpose flour, ⅓ cup powdered sugar, 2 tablespoons cornstarch, and ¼ teaspoon salt.
Add the flour mixture to the butter mixture in 3 parts, mixing between each addition just until incorporated. The dough will be mixed but slightly crumbly.
Transfer the dough to the prepared baking pan and press it evenly into the bottom of the pan.
Prick the surface of the dough all over with a fork. Pricking the shortbread frees steam while baking and prevents air bubbles.
Chill the shortbread in the refrigerator for 30 minutes.
With 15 minutes left of chilling, preheat the oven to 325°F.
After chilling, bake for 35 minutes.
While the shortbread bakes, pinch together the 2 tablespoons granulated sugar and 1 tablespoon lemon zest in a small prep bowl to infuse and then sprinkle over the top of the shortbread immediately after coming out of the oven after the 35 minutes of baking time is up. (See notes for alternative toppings)
Return to the oven and bake for 5 to 10 additional minutes until the tops and edges of the shortbread should be just turning golden brown.
Transfer the pan to a wire rack to cool, then use a sharp knife to gently cut the shortbread in the pan. Don't cut too hard because you want to try and avoid cutting the parchment or damaging the pan. Shortbread is easier to cut when warm.
Let the shortbread cool completely before lifting out of the pan and enjoying. These will have the best flavor the day after making as the lemon will intensify with time.