Yes, Parmesan ice cream used to be a thing. It was actually popular, especially in the time of the American Revolution. George Washington himself enjoyed it and you can, too, because there's a recipe preserved in a 1789 cookbook. Why was Parmesan ice cream such a hit? Perhaps because the cheese was one of the few European ingredients that could survive the trans-Atlantic passage to the New World.
This is only one of 7 once-popular ice cream flavors featured by the food blog The Takeout. They include teaberry, which is still found in Pennsylvania, and butter brickle, which is a kind of toffee flavoring.
Photo of non-Parmesan ice cream by PickPik