Preheat oven to 300 degrees F. Line a 13x9x2-inch baking pan with heavy foil, extending foil over pan edges. Lightly grease foil; set aside.
In a bowl, stir together flour and cornstarch; set aside. In another bowl, combine powdered sugar and lemon peel. Pressing against side of bowl with a wooden spoon, work lemon peel into powdered sugar until sugar is yellow and very fragrant.* Set aside.
In a mixing bowl, combine butter, lemon juice, salt, and vanilla; beat with an electric mixer on medium speed until combined. Gradually beat in sugar mixture. Stir in flour mixture. With lightly floured fingers, press dough evenly into the prepared pan.
Bake about 40 minutes or until pale golden in color and edges begin to brown. Remove from oven. Immediately spoon Lemony Glaze over top and gently spread to evenly distribute the glaze. Let cool completely. Using the foil, lift the uncut bars out of the pan. Cut into bars. Arrange bars in jar; cover.
In a bowl; combine powdered sugar, lemon peel, lemon juice, light-color corn syrup, and vanilla. Whisk until smooth.