Start by whisking your egg yolks in a medium bowl until they’re just combined. Set this aside.
In a medium saucepan, combine the heavy cream, whole milk, sugar, and salt. Heat this mixture over medium heat, stirring occasionally to help the sugar dissolve. You want to heat it until you see small bubbles forming around the edges and steam rising from the surface – but don’t let it boil.
Take about 1 cup of the hot cream mixture and very slowly pour it into your egg yolks while whisking constantly. This slowly brings up the temperature of the eggs without scrambling them. Keep whisking as you pour!
Pour this warmed egg mixture back into your saucepan with the remaining cream mixture, whisking as you go. Cook over medium-low heat, stirring constantly with a wooden spoon or silicone spatula. You’ll know it’s ready when the custard coats the back of your spoon and holds a clear line when you run your finger through it – this usually takes 4-6 minutes.
Pour the custard through a fine-mesh strainer into a clean bowl. Stir in the vanilla extract while it’s still hot.
Whisk in the dry cake mix while the custard is still warm. Keep whisking until there are no lumps. If you wait until it’s cold, you’ll end up with floury lumps.
Cover the surface directly with plastic wrap and refrigerate until completely cold, at least 4 hours or overnight.
When you’re ready to churn, pour the cold mixture into your ice cream maker. While it’s churning, mix the chopped white chocolate chips and rainbow sprinkles in a small bowl – combining them makes them easier to add evenly.
Churn according to your machine’s instructions – usually about 20-25 minutes. You’re looking for a soft-serve consistency. In the last minute of churning, pour in your sprinkle and white chocolate mixture.
Transfer to a freezer container, pressing plastic wrap directly on the surface of the ice cream. Freeze until firm, about 4 hours. The ice cream will keep getting harder over time.