Coincidentally, Sara Moulton just made eggnog with melted Hagen Daz vanilla ice cream. She added rum and a bit of grated nutmeg to the top.
The only time I ever made eggnog was when I was…22, first Christmas with MrsT and her family.
“The women” had all gone out to shop, and her dad and I proceeded to…get in the festive spirit, and before long, we were

-faced and he decided we needed eggnog.
Neither of us had a clue as to what was actually in eggnog, and this was before the internet, so…we just started combining noggy things - “Well, it’s gotta have eggs, right?! Put some eggs in there! And milk…or cream! And pour this in!”
We just kept going, and tasting, and it never quite tasted right, and finally, he dug into the freezer and popped out with a tub of vanilla ice cream…and dumped the whole thing in.
It tasted ok, as much as I can remember, but it didn’t taste like eggnog, and my god, that’s the only time I ever saw MrsT’s mom angry.