There are lots of ice cream recipes in the world. This is what I use because I prefer the richer taste of custard. What makes this "custard" is that it has eggs in it. It's basically a thin pudding that you freeze.
You can add anything to this to make your favorite flavors. 1/2 C of Cherry Jam makes this Cherry Custard. A chopped up banana and 1/4 cup of shredded coconut and you have a desert that tastes like a combination of coconut and banana cream pie. Wait until near the end of the freezing process, drop in a 1/2 C of drained maraschino cherries and you have Whitehouse. Experiment. Even your failures will be great. Enjoy.
Mix 1/2 and 1/2, milk, cornstarch, sugar, salt and butter in a saucepan and bring to a simmer over medium heat. The mixture will thicken. Turn off the heat.
In a bowl, whisk the eggs until light yellow. Temper the eggs, then combine with the main body of the cream mixture.
Over medium heat, stirring constantly, bring the custard barely to a simmer (do NOT boil hard) and hold there as it thickens (about 30 seconds or so). It will coat the back of a spoon. Take off the heat. Cool for 5-10 minutes. Stir in the vanilla.
Put in a bowl in the refrigerator for a few hours (at least 4 is best, but if you can't wait, get it as cold as you can as quickly as you can), although overnight is best. Stir occasionally to prevent a skin from forming, or to mix back in if you get one. (A skin on this won't kill you, just some textural interest).
Freeze in an ice cream maker according to your maker's directions.
This makes about a quart of frozen custard once you add any flavors, and works well in my one quart Krups ice cream maker. I just got a great deal on a Cuisinart 2 qt. ice cream maker. I multiplied the recipe by 1 1/2, and it worked great.
Why not multiply by two you ask? Running the ice cream maker at full capacity pushes it AND sometimes, if the custard mix wasn't cold enough OR I was sloppy with measuring and made a little too much OR I added to many extra little yummies, it would not freeze completely before the ice cream maker had given up its full cold. The mix finishes up fine in the freezer, but I'm finding that if I make it easier on the machine, the ice cream/custard is just that much better.
Tapioca starch (or flour) has less "flavor" than either corn starch or flour and thickens at a lower temperature, as long as you don't cook the heck out of it, which we are definitely avoiding in this recipe. This, by the way, is NOT instant tapioca, the little granules used for thickening pies and puddings, but a powder. I found mine in with the specialty flours (soy flour, rice flour) or it might be with the other thickeners (corn starch, arrowroot).