Ok, here's the link to the NYT Master Ice Cream recipe. I also added it to the original post. You'll notice mine is doubled to make 1/2 gallon and I don't futz around tempering the eggs the way they suggest. I just cook them low and slow with lots and lots of stirring. I've never made unintentional scrambled eggs yet!
I was always taught that a custard based ice cream IS ice cream and everything else is just frozen milk. My husband got me the churn this past Christmas and was very confused about why I needed to use eggs, why I needed to cook the base, and then told me he wouldn't be eating any of this gross custard stuff. Several hours later he was found in the kitchen licking the churn beater and saying how good it was.
Another egg-heavy recipe I like is Baked French Toast. I make a loaf of bread that uses a lot of eggs (like Challah), leave it out overnight uncovered, and then use it for the recipe the next day. It makes more than we can eat before it spoils, so I cut it into squares, wrap in foil, and freeze. It makes for a quick breakfast.
Another is "Baked Eggs". Layer toast in a casserole dish, top with a mixture of whatever cooked meat you have on hand (crumbled sausage, diced ham, etc) and veggies (we use diced tomatoes and fresh spinach), then crack 6 eggs on top. Bake until the egg whites are done - sometimes I turn on the broiler to finish them the last little bit.