Step 1
Prepare the Crust: Preheat oven to 350°F. Grease an 8-inch square baking pan with cooking spray; line bottom and sides of pan with aluminum foil, leaving a 2-inch overhang on all sides.
Step 2
Process all-purpose flour, sugar, rice flour, and salt in a food processor until well combined, about 5 pulses. Add butter and vanilla; pulse just until a dough ball forms, about 30 pulses. Press dough into an even layer in prepared baking pan, very lightly greasing hands with cooking spray, if needed.
Step 3
Bake in preheated oven until evenly golden brown, 24 to 28 minutes.
Step 4
While Crust bakes, prepare the Lemon Custard: Whisk together lemon zest and juice, salt, and 3/4 cup of the sugar in a medium saucepan until well combined. Heat over medium, stirring occasionally, until sugar dissolves and mixture is steaming, about 4 minutes.
Step 5
Meanwhile, whisk together egg yolks, eggs, rice flour, and remaining 1/4 cup sugar in a medium bowl until well combined. Gradually add hot lemon juice mixture to egg mixture, whisking constantly, until combined; add mixture to saucepan. Cook over medium-low, whisking constantly, until mixture coats the back of a spoon (it should hold a trail when a finger is run through) and an instant-read thermometer registers 175°F to 180°F, 2 to 4 minutes. Remove from heat.
Step 6
Gradually whisk in butter, a few cubes at a time, until melted and well combined. Strain mixture through a fine mesh strainer into a medium bowl, pressing through as much custard as possible; discard strained solids. Loosely cover Lemon Custard, if needed, until Crust is ready.
Step 7
Spread Lemon Custard in an even layer over hot Crust using a small offset spatula. Bake at 350°F until edges are slightly puffed and somewhat matte and Lemon Custard is mostly set, 10 to 12 minutes. (Custard may jiggle slightly as a whole.) Remove from oven, and let cool slightly in baking pan on a wire rack at room temperature, about 1 hour. Chill, uncovered, in refrigerator until completely cool, at least 1 hour or up to 12 hours. (If chilling for longer periods of time, loosely cover bars with aluminum foil once completely cool; see Note.)
Step 8
Run a sharp knife around edges to loosen bars from baking pan; using excess aluminum foil as handles, remove bars from pan. Trim edges if desired, and cut into 16 (1 3/4-inch) bars using a large sharp knife, wiping blade clean between cuts. Dust bars with powdered sugar just before serving.