Prepare your ice cream maker as needed. For some, that may mean freezing your insert for at least 24 hours.
Make a large bowl of ice water that is mostly ice. and Take our a large gallon freezer bag.
Mix together the milk, heavy cream, and half the sugar together in a large saucepan.
Stir well, preferably with a wooden spoon, and heat on medium-high heat. Continue stirring until the mixture is steaming and small bubbles form on the edges, but do not allow it to boil.
Mix together the salt, corn syrup, egg yolks, corn starch, and remaining sugar together in a small bowl.
Gently stir in one cup of the hot milk mixture into the egg mixture, beating well as you pour.
Slowly drizzle the egg mixture into the saucepan while stirring well.
Stir the mixture, scraping the sides and bottom of the saucepan to prevent the milk burning. Continue to cook until the mixture thickens. You will know it is finished when you can run a finger down the back of your wooden spoon and a line remains.
Stir in the cake mix.
Carefully pour the ice cream base into the gallon bag. Sit the bag in the ice water, leaving the top of the bag mostly open, but taking care that no ice water gets into the bag. Allow it to cool completely.
Add in the vanilla.
Place the cooled ice cream base into the refrigerator to cool completely.
Add the ice cream into the ice cream machine and churn according to manufacturer instructions (you may need to do this in batches). Five minutes before you are finished churning, add in the sprinkles.
Store the ice cream in an airtight container.
Notes
Do not let the gallon bag close all the way before the ice cream base is chilled, we want the steam to be able to escape. Check out the blog post for add-in ideas, plus other important tips and answers to common questions. If your question isn't answered, comment below!