Preheat oven to 325F/160C degrees. Grease or line a 9×13-inch pan with parchment paper or foil, leaving enough overhang on the sides for lifting the bars out of the pan after baking. Set aside.

To make the shortbread crust: Process flour, sugar, and salt in a food processor until combined. Add butter and vanilla and pulse until mixture becomes crumbly and resembles coarse meal. Alternatively, you can crumble all the ingredients together in a bowl using a pastry cutter. Sprinkle mixture into prepared pan and press firmly into an even layer. Bake for 18-20 minutes, until the edges are very slightly browned. Allow to cool on a wire rack just until warm, meanwhile make the filling.

To make the filling: In a large bowl, mix together sugar and lemon zest until well combined. Add eggs and whisk well until combined. Mix in lemon juice. Add flour and whisk until smooth. Pour into warm crust. Bake for 22-25 minutes, just until set and filling feels slightly firm to the touch. Allow to cool completely on a wire rack in room temperature, then refrigerate for at least 2 hours (preferably more or overnight) or until completely set. Then, lift the bars out of the pan using the parchment paper and cut into squares. Dust with powdered sugar.