We're in Tuscany, Maud, about 90 mins by train south of Florence, between Arezzo and Cortona.
C. Fiorentino is the better of the two Costolutos, I think. More of a beefsteak variety. C. Genovese is flatter and even more heavily ribbed. They're old Italian varieties but I suspect there has been some fiddling over the years. Neither has the full flavour they used to have. Still, of the two, you have the right one.