This rich, creamy concoction is pretty lethal in terms of calories and sugar, so keep servings small. A six-ounce serving has over 19 grams of sugar, as far as I can figure, so small cups and servings of four-five ounces are better all around. This tends to be one of those "love it or hate it" recipes, but the vast, vast majority of people LOVE it.
This is a very simple recipe in terms of the number of ingredients, but you need to get good quality ones (see my rant below on ice cream) and you need to plan ahead so that the ice cream is softened in time. I take the ice cream out of the freezer and put it in the fridge several hours ahead. Then about an hour before serving I go ahead and dump the ice cream into the punchbowl so that when I'm ready to serve it's very soft.
Stir the ice cream until it's smooth, then slowly stir in the eggnog. You don't want lumps. Then slowly stir in the ginger ale. It does foam up quite a bit, so persevere. If it sits for very long it'll get a layer of foam on the top which needs to be stirred back in. If you're serving the punch instead of having people help themselves you'll be able to keep stirring it, but if you leave it as a self-serve item you might want to check back periodically or encourage people to stir the punch before they take some. No big deal, though.
Use the smallest punch cups you can; the six-ounce size is the best, as then you'll only be able to put in four-five ounces.
*Please, please, please--do not use that horrible cheap ice cream that comes in the big tubs for this recipe! (Actually, don't use it at all, for anything.) It's mostly air. You'll be very disappointed in the results, as the punch will be very foamy and not very creamy. If you don't want to spend the money on good ice cream, make some other kind of punch. Peppermint ice cream can be hard to find, but there are usually a few companies that come out with that flavor for the holidays--Edy's or Dreyer's (same ice cream, different brand in different parts of the country), or, the best because it comes in true half gallons, Blue Bell. Most ice cream these days comes in 1.75 or 1.5 quart sizes, and you have to figure out how to come out with a half gallon--2 full quarts--in your punchbowl. So very much easier to have a half-gallons size to begin with! If you're stuck with the smaller sizes, you'll just have to cope. Again, if you don't want to bother, make something else. I've cheated before with the smaller-size carton, thinking that it wouldn't make much difference, but it does. For the 1.75 quart size you'll need 8 additional ounces for each batch from another carton, or 1/7 of that container. The 1.5 quart container is actually easier to deal with, as you need one additional third of a carton. You can do some kind of pre-measuring if so desired, especially if you're making a lot. Anyway, as is probably evident, this recipe is only for the obsessed!