It is a traditional cake produced almost all over Italy where you can find chestnut woods. In any other part of Italy (from Piemonte to the Campania hinterland) you call it “Castagnaccio”. ONLY within the Province of Arezzo (Pratomagno mountain and Casentino valley) you find it named as BALDINO.
The name seems to be very used among the Longobardian feudatories in the period of their decadence and in the following retirement in the mountain castles (from Wald to Baldi or Baldini) who became then also the owners of water mills for milling chestnuts.
The chestnut represented an excellent solution for the poorest people against indigence and hunger.
The “dried” chestnut and the flour obtained by its milling (mixed with the grain one or all alone), became the daily  “bread” in certain areas.
One of the most important duties for women in the mountain houses was that to provide to the preparation and cooking of the Polenta by sharing its still hot slices by starting from the had of family; during the holidays, if the grain flour bread missed you could provide to knead the Baldino, made of chestnut flour melted in hot water to which you could add some pineseeds, rosemary leaves, a little olive oil when you had it or even some spoon full of pork fat lard melted, that was easier and cheaper to keep.
It is a product distributed in winter months when it’s time to harvest chestnuts (since October to November) until February when the chestnut flour is still fresh and perfumed; then the falling period starts (from February onwards). 
You can find it all over the province of Arezzo especially in mountain areas:
Pratomagno, the whole Casentino Valley, the Tuscan tevere Valley and the Upper Arno Valley.