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.

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.

Bake in preheated oven until evenly golden brown, 24 to 28 minutes.

While Crust bakes, prepare the Lemon Custard: Whisk together lemon zest and juice, salt, and ¾ 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.

Meanwhile, whisk together egg yolks, eggs, rice flour, and remaining ¼ 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.

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.

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.)

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 ¾-inch) bars using a large sharp knife, wiping blade clean between cuts. Dust bars with powdered sugar just before serving.