Oil or spray an 8 X 11 glass baking dish.
In a medium heatproof bowl, stir cornstarch with 1/2 cup of the sugar. Slowly whisk in 1 cup milk. Add egg yolks and 1 of the whole eggs and whisk until smooth. Whisk in 1/4 teaspoon of the cinnamon.
Over moderate heat, heat 3 cups of milk until small bubbles form around edge in a medium saucepan. Gradually whisk the hot milk into the egg mixture. Return the mixture to the saucepan and cook over moderate heat, whisking constantly, until the consistency is thicker than mayonnaise, about 5 minutes. Stir in the vanilla.
Scrape custard into oiled baking dish and smooth the surface; let cool slightly. Refrigerate until very firm, at least 3 hours or overnight.
In a small bowl, combine the 1/2 cup of sugar with the 2 tablespoons of cinnamon.
In a pie plate, whisk 2 eggs and 2 tablespoons of milk.
Spread the flour in another pie plate.
Cut the custard into 24 rectangles.
In a large, deep nonstick skillet, heat 1/2 inch of vegetable oil until shimmering. Working with 6 pieces of custard at a time and keeping the rest refrigerated, dip the custard rectangles in the beaten eggs, then dredge in the flour. Fry the custard over moderate heat, turning once or twice, until golden and crisp, about 5 minutes. Transfer to a rack lined with paper towels and immediately sift cinnamon sugar over them.
Repeat with the remaining pieces of custard. Serve warm or at room temperature.