Preheat the oven to 350°F. Grease an 8x8-inch baking dish.
In a medium bowl, combine the flour and powdered sugar. Cut in the softened butter until the mixture resembles coarse crumbs.
Press the mixture into the bottom of the prepared baking dish to form a crust. Bake for 15 minutes or until lightly golden.
While the crust is baking, whisk together the granulated sugar, eggs, lemon juice, lemon zest, baking powder, and salt in a separate bowl until well combined.
Pour the lemon mixture over the hot crust and return to the oven. Bake for an additional 20-25 minutes, or until the filling is set and the edges are lightly golden.
Remove from the oven and let cool completely in the baking dish. Once cooled, dust with powdered sugar and cut into squares.