Put raisins in a bowl and add warm water to cover. Soak until raisins are plumped, about 15 minutes. Drain and pat dry.
In a large bowl, combine the capon, celery, pomegranate seeds, pistachio nuts, and soaked raisins; mix well. In a bowl, combine the olive oil and vinegars, whisking to emulsify. Pour over the salad and season with salt and pepper. Mound the capon salad on a serving platter. Top the salad with the Parmigiano-Reggiano shavings, if desired.