Preheat oven to 350 degrees with a rack in the center of oven. Butter a 9-by-13-inch baking pan.
To make crust: In the bowl of a food processor, combine flour, confectioners' sugar, cornstarch, and salt; process to combine. Add butter to processor and process until mixture is pale yellow and resembles a coarse meal, about 10 seconds. If you don't have a food processor, whisk together flour, confectioners' sugar, cornstarch, and salt in a large bowl. Add butter and work into flour mixture using a pastry blender or your fingers.
Pour crust mixture into prepared baking dish, pressing down with your fingers to create a 1/4-inch-thick layer along the bottom and 1/2-inch up the sides, pressing firmly at the edges to seal. But do not over press the entire pan, you don't want the crust to be overworked and chewy. Transfer pan to freezer and freeze for 30 minutes. Transfer to oven and bake, rotating pan once during baking, until golden brown, about 20 minutes.
Meanwhile, make the topping: In a large bowl, whisk together sugar and lemon juice, add flour, milk, and salt until well combined, then gently stir in beaten eggs. Do not over beat the eggs or they will be foamy.
Remove baking pan from oven. Stir topping and pour into warm crust. Return pan to oven and continue baking until topping is just set but not browned, about 20 minutes.
Transfer baking pan to a wire rack to cool completely. Cut into 20 squares. Serve immediately or wrap each bar tightly with plastic wrap and keep refrigerated until ready to serve.