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The answer, at least a partial one: eggs. Eggs, specifically egg yolks, play several roles in homemade ice cream. You can make tasty ice cream without them, but there's a reason that almost every recipe published in the last 50 years calls for them. After water, egg yolks are mostly fat and protein.
The best/only way I have found to hard cook fresh--1 or 2 day old eggs--that allows for them to be peeled cleanly, is to steam, not boil them. Put eggs in a basket over about 2 of water. Bring to a boil, cover and cook on medium heat so steam continues for about 20 minutes. Prepare an ice water bath as eggs steam. At the 20 minute mark remove basket and put basket with eggs in the ice water. Peel them in the ice water.