In the bowl of a stand mixer fitted with a paddle attachment, cream the butter until smooth, about 2 minutes. Add the sugar and continue creaming until light and fluffy, an additional 2 minutes. Add the eggs, one at a time, beating between each addition, then beat in the vanilla extract, scraping down the sides as needed.
Add the flour, baking powder and salt and beat just until combined.
Remove the dough from the mixer, divide it in half and shape each piece of dough into a flat square. Wrap each square securely in plastic wrap and refrigerate them for 1 hour.
Place each piece of dough between two sheets of parchment paper. Using a rolling pin, roll each piece of dough until it is a rectangle measuring roughly 14x11 inches. Square off the bottom edge.