But are you interested in the recipe or only in the name of drink? Because I am italian but I don't know the name used out of Italy.

Here is a link that might be useful: Croce & Delizia

Espresso and half and half is my favorite drink, but I can't imagine why you'd add the half and half after pouring it over ice. The ice would melt a ton and you'd get a watery drink-- the half and half cools down the espresso, and then you scoop the ice in or pour it over ice.

But if you want that, and you're wondering how to order it, I'd just order an iced espresso shot (or double, or whatever) and add the half and half from the milk bar.