Winter Chicory Salad with Kumquats and Date Dressing

1/2 cup extra-virgin olive oil

3 tablespoons sherry vinegar

3 tablespoons fresh orange juice

1 tablespoon finely chopped shallot

2 cups kumquats, sliced into 1/8-inch rounds, seeds removed, divided

1/2 cup dried pitted dates, thinly sliced, divided

1 teaspoon kosher salt, divided

1/2 teaspoon black pepper, divided

4 Belgian endive leaves, sliced (about 1 cup)

2 cups bright yellow frisée leaves (from 1 large head, use yellow leaves only)

2 cups packed fresh arugula

1 cup packed fresh mizuna

1 cup sliced Treviso or Chioggia radicchio

1/2 cup loosely packed fresh flat-leaf parsley leaves

1 tablespoon fresh mint leaves, cut into thin strips

1/2 cup toasted salted pistachios

4 ounces aged pecorino Romano cheese, shaved with a Y-shaped vegetable peeler (about 2 cups)