Preheat your oven to 350 degrees Fahrenheit. This step is crucial for ensuring that your crust bakes evenly. Grease a 9 by 13 pan and set aside to prepare for the buttery crust.
In a large mixing bowl, use a hand mixer to beat the butter and confectioners' sugar together until they are well blended. You want the mixture to be creamy and smooth, which should take about 2 to 3 minutes.
Slowly add in 1 and 1/2 cups of all-purpose flour to the butter mixture. Mix until fully incorporated, creating a soft dough. This dough will form the lovely base of your bars.
Press the dough firmly into the bottom of your greased pan. Make sure to spread it evenly for consistent baking. Bake in the preheated oven for 18 to 20 minutes, or until it's golden brown around the edges.
While the crust is baking, prepare the lemon filling. In a small bowl, whisk together the eggs, granulated sugar, lemon zest, lemon juice, milk, and the remaining 3 tablespoons of flour until the mixture is frothy. This step is key to ensuring a light and airy filling.
Once your crust is out of the oven and slightly cooled, pour the lemon filling over the hot crust. This will help the filling set better as it bakes.
Reduce the oven temperature to 325 degrees Fahrenheit and return the pan to the oven. Bake for an additional 18 to 20 minutes until the top is lightly browned and set. Keep an eye on it to avoid overbaking!
Once done, remove the pan from the oven and allow it to cool completely on a wire rack. This step is important as it helps the filling further firm up.
After cooling, dust the top with additional confectioners' sugar for that classic finish. Cut into bars and refrigerate any leftovers, though I doubt there will be many!