The lemon filling must be added to a warm crust. The 30-minute chilling and 20-minute baking of the crust should allow plenty of time to prepare the filling. If not, make the filling first and stir to blend just before pouring it into the crust. Any leftover bars can be sealed in plastic wrap and refrigerated for up to two days.
1. For the crust: Adjust oven rack to middle position and heat oven to 350 degrees. Lightly butter a 13-by-9-inch baking dish and line with one sheet parchment or wax paper. Dot paper with butter, then lay second sheet crosswise over it (see illustration 1, below).
2. Pulse flour, confectioners’ sugar, cornstarch, and salt in food processor workbowl fitted with steel blade. Add butter and process to blend, 8 to 10 seconds, then pulse until mixture is pale yellow and resembles coarse meal, about three 1-second bursts. (To do this by hand, mix flour, confectioners’ sugar, cornstarch, and salt in medium bowl. Freeze butter and grate it on large holes of box grater into flour mixture. Toss butter pieces to coat. Rub pieces between your fingers for a minute, until flour turns pale yellow and coarse.) Sprinkle mixture into lined pan and, following illustration 2, press firmly with fingers into even, 1/4-inch layer over entire pan bottom and about 1/2-inch up sides. Refrigerate for 30 minutes, then bake until golden brown, about 20 minutes.
3. For the filling: Meanwhile, whisk eggs, sugar, and flour in medium bowl, then stir in lemon zest, juice, milk, and salt to blend well.
4. To finish the bars: Reduce oven temperature to 325 degrees. Stir filling mixture to reblend; pour into warm crust. Bake until filling feels firm when touched lightly, about 20 minutes. Transfer pan to wire rack; cool to near room temperature, at least 30 minutes. Following illustrations 3 and 4, below, transfer to cutting board, fold paper down, and cut into serving-size bars, wiping knife or pizza cutter clean between cuts, as necessary. Sieve confectioners’ sugar over bars, if desired.