To make the crust: Mix the flour and brown sugar in a food processor until it is fully blended.
Add the butter pieces to the flour mixture and pulse the food processor until the butter is cut into tiny, pea-sized pieces and the dough looks lumpy.
Pour crust mixture evenly into an ungreased 9x13 baking dish. Press the crust down, with a spatula, to make it packed.
Bake crust in oven until golden brown, about 20 minutes.
While the crust is baking, make your lemon topping: In a medium bowl, use an electric mixer to beat the eggs until they are well blended.
Add the vanilla extract and ½ cup of the powdered sugar, then mix well.
Add the lemon juice and the rest of the powdered sugar. Mix until the powdered sugar is completely dissolved and then add the lemon zest.
As soon as the crust is finished, take it out of the oven and reduce the temperature to 300.
Immediately pour your lemon topping over the hot crust and continue to bake for 30 minutes.
Cool and cut into 24 bars.
Bakers frequently fail when pouring cold curd onto a cool crust, which prevents the eggs from setting uniformly and leads to a runny center. Temperature management dictates the structural integrity of citrus squares. Cold butter must be pulsed into all-purpose flour until particles resemble small peas. This solid fat creates flaky pockets when exposed to 350 degrees Fahrenheit. Pressing the crumb firmly into an ungreased 9x13 baking dish ensures the base holds together without excess grease pooling underneath. Baking the foundation for twenty minutes develops the necessary starches to support a heavy liquid layer. Pouring the egg and lemon mixture directly onto the hot crust accelerates the thermal setting process. Dropping the oven temperature to 300 degrees immediately afterward allows the custard to firm up gently over thirty minutes without scorching the dairy solids. Fresh citrus juice provides acidity that reacts with the protein matrix of four large eggs. Sifting powdered sugar into the liquid prevents lumps from forming in the filling. Leaving out optional lemon zest reduces the sharpness of the overall profile for a milder taste. Chilling the finished bars for two hours firms the butter fats and allows clean slicing with a sharp knife. Store leftovers in a sealed container in the refrigerator for up to four days. Pairing these tart pieces with unsweetened black coffee or hot green tea balances the intense sugar content on the palate.