Preheat oven to 350°F (177°C). Line an 8x8" pan with parchment, leaving overhang for easy removal.
In a bowl, whisk together flour, cornstarch, sugar, and salt. Using a pastry cutter, a fork or your hands cut in cold butter until the mixture resembles fine crumbs. Mix in vanilla just until combined.
Press evenly into the pan. Bake 18–20 minutes, until edges are lightly golden.
In a bowl, combine the sugar and lemon zest and using your fingers rub together until fragrant and pale yellow. Whisk in the flour. Add eggs one at a time, whisking gently until smooth. Stir in the lemon juice and salt.
Immediately pour the filling over the hot crust, then gently tap the pan on the counter to release any air bubbles.
Reduce oven to 325°F (163°C) and bake 20–25 minutes, until center is just set (no jiggle).
Cool completely at room temperature then chill for at least 2 hours in the refrigerator. Using the parchment paper overhang lift the bars out of the pan, slice, and dust generously with powdered sugar.
