What makes these potatoes Venetian is simply the frequency with which I have seen them prepared in this manner in the homes of Giardini. The shape of the cut potatoes sometimes varies (thick disks are quite popular) but I much prefer the dice shape. The consistent features are the melted onions and the unctuous syrupy stock sauce. I wouldn’t worry too much about the type of potato, either. With waxy varieties, the dice holds its shape much better and the slightly yellow hue is a little more attractive. But floury spuds disintegrate a tad more, so the sauce has more viscosity, giving a fuller, deeper flavor. I love them both ways.