We did some experimenting in the kitchen and discovered one great way to make cake batter ice cream (there may be more)...

We used a sweet cream base from the Ben & Jerry's Ice Cream Cookbook.

We stuck it into the ice cream maker and as it was freezing (mostly near the beginning because you have to make sure the flour doesn't clump) we put in some yellow cake mix. For a recipe that makes a quart, we threw in a little more than a half cup. (About 2 tablespoons extra) You can modify that to your own taste, but that is what we thought tasted good. It may be too much for some people.

Hope that helps.
Bon Apetit!