Preheat oven to 350°F (180°C). Line an 8-inch square baking pan with foil, letting excess extend over all sides of pan. Lightly spray foil with baking spray with flour.
For crust: In a large bowl, whisk together flour, confectioners’ sugar, and salt. Add melted butter; stir until combined and a dough forms. Press into bottom of prepared pan.
Bake until crust is set and edges are golden brown, 18 to 20 minutes. Reduce oven temperature to 300°F (150°C).
Meanwhile, for filling: In a medium bowl, whisk together granulated sugar, flour, lemon zest, and salt. Add eggs, lemon juice, and vanilla, and whisk until smooth. Pour onto hot crust.
Bake until edges of filling are set, center jiggles slightly, and an instant-read thermometer inserted in center of filling registers 175°F (79°C), 25 to 30 minutes. Let cool completely in pan on a wire rack. Refrigerate until cold and firm, about 2 hours.
Using excess foil as handles, remove from pan, and cut into bars. Dust with confectioners’ sugar just before serving. Refrigerate in an airtight container for up to 3 days.