Preheat the oven to 350°. Position a rack in the lower third of the oven.
To make the crust: Cut butter into chunks and melt it in a medium saucepan over medium heat. Remove from the heat and stir in the sugar, vanilla, and salt. Add the flour and mix just until incorporated. Press the dough evenly over the bottom of the pan, Bake for 25- 30 minutes, or until the crust is well browned at the edges and lightly browned in the center.
To make topping: While the crust is baking, stir together the sugar and flour in a medium bowl until well mixed. Whisk in the eggs. Stir in the lemon zest and juice. When the crust is ready, turn the oven down to 300 and slide the rack out without removing the pan. Pour the filling over the hot crust.
Bake for 20- 25 minutes, or until the topping is puffed at the edges and no longer jiggles in the center when the pan is tapped. Set on a rack to cool completely in the pan. Lift the ends of the foil liner and transfer to a cutting board. Use a long sharp knife to cut into sixteen 2 inch bars. May be stored, airtight, in the refrigerator. Lemon bars keep perfectly for about 3 days; after 3 days the crust softens but the bars still taste quite good for the remainder of a week. Do not freeze. Sieve powdered sugar over the bars just before serving.
Equipment: 8-inch square pan, lined on the bottom and up all 4 sides with foil.