In Trento and in Florence, I ate a dessert the waiters called profiterrol (spell?).

In the United States, if you ask for such a dessert you are served something like a doughnut stuffed with ice cream and drizzled with chocolate sauce....ugh! \

the beautiful thing I ate in Florence was also a round doughnut shell, but filled with vanilla cream and the outside was completely coated with a chocolate like cream/icing.

does anyone know what this is called - outside of Trento, Verona and Florence?

Thank you very much.

You're right, it's called profitterol. About the spelling, I think it's a French name; however it is the word used in the whole country.
Cheers,