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Parmigiano-Reggiano,
Grana Padano, is a hard cheese ideal for grating or shaving over foods. Both are staples of the Italian kitchen, but Grana is generally more grainy (hence the name) and less salty. Either one works well in this salad.
Most of the vinaigrette ingredients may be mixed several hours ahead, but add the chopped mint just before serving to preserve its color and texture.