Preheat the oven to 350°F. Grease an 8x8-inch baking dish and line it with parchment paper on all sides. Leave an overhang on at least two sides of the pan to help you remove the bars after baking.

Make the shortbread crust: In a large bowl, whisk together the flour, powdered sugar, and salt. Add the melted butter and vanilla and use a spatula to mix until a greasy dough forms. Transfer the dough to the prepared pan and use your hands to press it evenly over the bottom and ⅛-inch up the sides.

Bake the crust for 18 to 20 minutes, or until lightly browned around the edges. Remove from the oven and dock with a fork.

Meanwhile, make the lemon filling: Place the sugar in a large bowl. If using the lemon zest, add it to the bowl and use your fingers to work it into the sugar to release its fragrant oils.

Add the flour and whisk to combine, then whisk in the eggs followed by the lemon juice.

Pour over the hot crust and bake for 20 to 25 minutes, or until the filling is set. It should no longer jiggle when you gently shake the pan.

Remove from the oven and let cool for 1 hour at room temperature. Transfer to the refrigerator and chill for another 2 hours.

Dust the chilled bars with powdered sugar, slice, and serve.