Whisk the eggs and cake batter together in a bowl. It will become thick and lumpy.
In a medium saucepan over medium-low heat, heat the milk and cream until edges just begin to bubble. Carefully whisk into the egg yolk mixture, making sure to break up any lumps. Return the mixture to the saucepan over medium heat again until thick enough to coat a spoon, about 3 minutes, whisking constantly.
Set in a fresh bowl over an ice bath and whisk in the vodka, whisking to lower the temperature. Cover and place in fridge until completely chilled 6 – 8 hours.
When ready to churn the ice cream, chop up the cake and have it and extra sprinkles ready to go. Churn the cream mixture according to manufactures directions. When almost set, add the cake, crumbs and all. Spoon into a resealable container, randomly tossing in sprinkles here and there. Seal and freeze over night.
Serve with sprinkles on top. Because you can really never have enough sprinkles…