Preheat oven to 350°F (175°C). Line a 9x13" (23x33cm) baking pan with parchment paper with an overhang on all sides. Set aside.
Make the shortbread crust in a food processor: Place flour, sugar, salt, and butter in a food processor and pulse a few times just until it starts to clump.
If you don't have a food processor, then make the shortbread crust with a pastry cutter or two forks instead: In this case mix together flour, salt, and sugar in a large mixing bowl. Then add butter and cut it into the mixture until it starts to clump.
Transfer crust to the prepared baking pan and press with your fingers evenly into the bottom of the pan. Place a piece of paper on top and flatten the crust with the back of a flat-bottomed cup. Bake for 20 minutes until crust is lightly browned.
While the crust is baking, prepare the filling: In a large mixing bowl, using a handheld or stand mixer fitted with a whisk or paddle attachment, mix eggs, sugar, and lemon zest on medium speed until creamy and sugar is completely dissolved, about 2-3 minutes. Add flour and mix just until incorporated. On low speed, slowly stir in lemon juice just until combined. Pour onto crust. Bake for about 35-40 minutes or until filling is almost set with a very slight wobble in the center. Cover with parchment paper after the first 20 minutes to prevent browning too much, if desired.
Remove from oven and let cool to room temperature. Then chill in the fridge overnight. Cut into 20 bars. Before serving, dust with powdered sugar. Store leftovers in the refrigerator in an airtight container for up to 3 days.