1. Preheat the oven to 350°. Line a heavy 8-inch square metal baking pan with foil.
2. Make the crust: In a medium bowl, combine the melted butter with the sugar, vanilla and salt. Add the flour and mix just until incorporated. Press the dough evenly over the bottom of the pan. Bake in the bottom third of the oven until the crust is well browned at the edges and golden brown in the center, about 25 minutes.
3. Meanwhile, make the topping: In a medium bowl, whisk the sugar and flour to mix. Whisk in the eggs until blended, then whisk in the lemon zest and juice.
4. Turn the oven down to 300°. Carefully slide the rack with the pan out and pour the filling onto the hot crust. Bake for 20 to 25 minutes longer, until the topping is puffed at the edge and no longer jiggles in the center. Transfer the pan to a rack and let cool completely then cut into bars/dust with powdered sugar.