Preheat oven to 350 degrees, with rack in center. Coat a 9-inch square baking pan with cooking spray; line pan with two crisscrossed rectangles of parchment paper, leaving a 2-inch overhang on all sides.
Make the crust: In a food processor, pulse flour with confectioners' sugar, cornstarch, and salt. Add butter; pulse until mixture resembles coarse crumbs. Press into bottom and 3/4 inch up sides of prepared pan. Refrigerate 15 minutes.
Bake until crust is lightly browned 20 minutes. Let cool slightly in pan. Reduce oven heat to 325 degrees.
Meanwhile, make the lemon filling: In a bowl, beat eggs with a whisk or with an electric mixer until thick. Beat in granulated sugar, lemon juice, flour, baking powder, and salt. Pour over warm crust. Bake until set, about 20 minutes. Cool to room temperature; refrigerate about 1 hour.
Using paper overhang as an aid, lift square from pan. Sift remaining tablespoon confectioners' sugar over the top. Cut into 16 squares