put dairy of the fat percentage that you want in the blender - 3 to 4 cups. You could probably use almond milk, and you can definitely use coconut milk – and a mix would be quite nice. I have never tried oat milk.
put sweetener of the kind you want (granulated sugar, brown sugar, palm sugar, sucralose, stevia…) in the blender. This is typically 3/4 to 1.5 cups depending on the quantity of dairy and the strength of other flavors.
add flavor components
add a little salt and a little alcohol - even if you aren't going for an alcohol-carried flavor, a splash of vodka breaks up ice crystals. Anything else is for flavor.
Whiz it until frothy and well-combined. Correct the flavors: you want it to be a very strong but not unpleasant flavor at this point, because you will be diluting it slightly with eggs and cold reduces flavor impact.
Add eggs, either whole or yolks. 1 per cup of dairy makes a nice custard, and you can go up to 2.5 per cup if you want a really custardy texture.
Whiz until it steams, typically 6-9 minutes at high speed. If you don't have a high-power blender, this will either burn out your motor or just not happen, so instead, blend it for a minute and then cook it in a double boiler until it thickens.
Cool it down: at least to ambient refrigerator, but just-above-freezing is better.
Put it in an ice cream freezer and churn.
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If I didn't have a Vitamix, this would be a process of carefully heating the dairy until the eggs were properly cooked into a custard; a double boiler would help.
Today's dairy is all half-and-half (we buy the half-gallons at Market Basket), the sweetener is sucralose, and the flavors are from dutched cocoa, a couple of tablespoons of Frangelico, a half cup of sugar-free hazelnut syrup (Torani makes a good one), and a glug of white rum. If I used dark rum, it would be half-to-two-thirds of a glug – more flavor.