Preheat the oven to 300°F.

Line the bottom and sides of a 9x13-inch baking dish with parchment paper. Set aside.

Place the butter and powdered sugar in a stand mixer bowl or large mixing bowl. Beat on low speed to blend, then switch to medium speed and beat until soft and light. Beat in the vanilla. Add the flour one cup at a time, mixing until fully combined. Scrape down the sides of the bowl as needed.

Press the dough into the prepared baking dish using a flat hand and fingers until dough is a smooth, even layer about 1/2-inch thick. With a fork, dock the dough across the short side of the dish in lines about 1 inch apart. Freeze for 5 minutes.

Bake the shortbread on middle rack of oven until golden, 35-45 minutes.

Check to see that shortbread is done. Remove from oven or add time as needed.

Cool shortbread on a cooling rack for 5 minutes.

Starting from a long side, cut the shortbread in the dish into 1-inch strips. Working from a short side, cut the strips into quarters to create rectangular cookies. Let cool completely in the dish, about 2 hours.

Gently remove cookies from dish using a small offset spatula. Serve immediately, or store in an airtight container at room temperature for 1 week, or freeze in an airtight container for up to 3 months.