The mayor told us that caterers for the excellent meal after the concert in Segusino were a small restaurant in the hills above the town in Milies di Segusino.  For all those who want to go back to find it, the address is:
Osteria Romolet
Via dei Ciclamini 4,
Milies di Segusino
Reservations: 0423 979400

Their card says:
Gilled food, on a spit, traditional cooking with local produce.
Lunch, dinner, buffet and refreshments.
Reservations are appreciated.