The tart flavor of the filling contrasts nicely with the rich, buttery crust. The squares can be refrigerated for up to 3 days, but bring them to room temperature before serving for the best flavor.
Position a rack in the lower third of the oven and preheat to 350 degrees F.
Sift the flour and confectioner's sugar into a medium bowl. Blend in the butter with your fingers until well-mixed. Pat evenly into an 8-inch square baking pan.
Bake until the crust is golden and set, 15 to 20 minutes.
Combine the eggs, sugar, baking powder, salt, and lemon juice in a medium bowl and whisk just enough to blend.
Pour the filling over the baked crust and return the pan to the oven. Bake until the filling is just set (it will still jiggle a bit in the center), 20 to 30 minutes. Cool in the pan on a wire rack.
To serve, sift confectioner's sugar over the pan and cut into squares.