Pickled Vegetable Salad with Nori Vinaigrette

Name: Pickled Vegetable Salad with Nori Vinaigrette
Ingredients: 6 radishes, trimmed, thinly sliced; 2 large carrots, peeled, julienned; 1/2 medium red onion, thinly sliced; 1/2 English hothouse cucumber, thinly sliced; 2 tablespoons sugar; 1 tablespoon kosher salt; 1 1/4 cups unseasoned rice vinegar, divided; 2 toasted nori sheets; 1/4 cup vegetable oil; 2 tablespoons reduced-sodium soy sauce; 1 tablespoon mirin (sweet Japanese rice wine); 5 ounces tender lettuces (such as Bibb, butter, and mâche; about 6 cups)