Place 1 1/3 cups flour, 1/4 cup white sugar, 1 tablespoon lemon zest, in a mixing bowl. Add the softened butter and mix with your hands until the mixture resembles coarse crumbs. Press into the bottom of a 9-inch square baking dish.
Bake in the preheated oven until the crust is golden brown, about 20 minutes.
While the crust is baking, stir together the brown sugar, 1/4 cup white sugar, 1 tablespoon flour, and the baking powder in a bowl. Add the eggs, lemon zest, and lemon juice; whisk until the sugars have dissolved; pour over the crust.
Return to the oven and bake until the lemon filling has firmed, about 15 minutes. Cool completely in the pan before cutting. Sprinkle Powdered sugar using a sifter on top.