Keep the oven preheated to 350° F. In the bowl of a stand mixer fitted with a whisk attachment, combine sugar and lemon zest and mix until well incorporated.
Add in the flour and salt and mix to combine. While the mixer is running, add the eggs one at a time, letting each egg get incorporated before adding the next one.
Stream in the lemon juice and continue mixing until combined. Add vanilla and mix until incorporated.
Pour the filling mixture into the prebaked crust and place into the preheated oven on the middle rack. Bake for 35 minutes, or until the center is almost set.
Once baked, remove from the oven and place on a wire cooling rack to let it completely cool.
Once the lemon bars have completely cooled, cover with plastic wrap and place into the fridge to let chill for 2 hours.
Once chilled, remove from the fridge and dust with powdered sugar and top with lemon slices before serving.