In a medium saucepan, whisk together all pudding ingredients, except for the vanilla. Turn the heat on medium and cook, stirring frequently, until thickened – about 7-9 minutes. After about 5 minutes, start to stir constantly. It will go from thin and watery to thick in a matter of seconds. Do not let the pudding boil! It's okay if it boils for a few seconds, but not more. Stir in the vanilla. It will be quite a bit thicker than regular pudding and will thicken even more as it cools. Set aside to cool while you prepare the cake. If you want to prevent a film from forming, cover with a piece of plastic wrap. I skip that step and just give it a good stir after it's cooled. There will still be some lumps, but you don't notice them in the finished cake.
2/3 cup (158 ml) milk of choice, 1 large egg yolk, 3 tablespoons granulated sugar, 2 tablespoons (16 grams) cornstarch, pinch salt, 1 teaspoon vanilla extract