Preheat oven to 325°F. Line an 8 x 8-inch pan with non-stick foil (or regular foil sprayed with cooking spray).
In a large bowl, combine the room-temperature butter, sugar, and powdered sugar. Using a hand mixer, beat on medium speed until light and creamy, about 2–3 minutes.
Add the vanilla and beat until combined.
Add the flour and mix on low speed just until the dough comes together; avoid overmixing.
Remove about one-third of the dough and set it aside in the refrigerator. Press the remaining two-thirds of the dough evenly into the prepared pan to form the bottom crust.
Bake the crust until slightly golden, about 20 minutes. Meanwhile keep the reserved dough chilled.
Remove the pan from the oven and crumble the reserved chilled dough evenly over the hot crust.
Return the pan to the oven and bake until the crumbled topping is firm and lightly golden, about 20–25 minutes.
Let the bars cool in the pan until cool to the touch (or cool completely). Refrigerate to speed cooling if desired, then cut into squares.