Stir together butter, 1/4 cup sugar, vanilla and salt.
Add one cup flour; mix just until incorporated. Press evenly into the bottom of an aluminum foil-lined 8"x8" baking pan.
Place a rack in the lower 1/3 of oven.
Bake at 350 degrees for 25 to 30 minutes, until edges are golden and center is lightly golden. While crust is baking, stir together remaining sugar and flour in a separate bowl.
Whisk in eggs; stir in lemon zest and juice. When baked crust is done, reduce oven temperature to 300 degrees. Pull out oven rack without removing pan; pour filling over hot crust.
Bake for 20 to 25 minutes longer, until topping is puffed at the edges and no longer jiggles in the center. Set pan on a wire rack; cool completely. Lift the ends of the foil; transfer to a cutting board.
Cut into bars with a long sharp knife. Keep bars refrigerated in an airtight container up to 3 days. Dust with powdered sugar at serving time.
