1. Whisk together olive oil, sherry vinegar, orange juice, shallot, 1 tablespoon kumquats, and 1 tablespoon dates until blended. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
2. Place the remaining kumquats and dates in a large bowl. Reserve and set aside 6 tablespoons vinaigrette. Drizzle remaining vinaigrette over kumquat mixture, and, using your hands, pull dates apart into individual slices. Add endive, frisée, arugula, mizuna, radicchio, parsley, and mint; gently toss to coat. Season with remaining 1/2 teaspoon salt and remaining 1/4 teaspoon pepper.
3 To serve, divide salad evenly among 6 plates; drizzle 1 tablespoon of the reserved vinaigrette over top and around each salad. Garnish with pistachios and shaved pecorino Romano.