6 radishes, trimmed, thinly sliced
2 large carrots, peeled, julienned
1/2 English hothouse cucumber, thinly sliced
2 TBSP sugar
1 TBSp salt
1 1/4 c unseasoned rice vinegar, divided
2 toasted nori sheets
1/4 c vegetable oil
2 TBSP soy sauce
1 TBSP rice vinegar
6 c lettuce
Place radishes, carrots, and cucumber in 4 separate bowls or jars. Bring sugar, salt, 1 c vinegar, and 2 c water to a boil in a medium saucepan, stirring to dissolve sugar. Pour pickling liquid over vegetables to cover; let cool. Cover and chill.
Grind nori in a blender, scraping down sides as needed, until finely ground. Add oil, soy sauce, mirin, and remaining 1/4 cup vinegar and blend until smooth. Toss lettuces and dressing in a large bowl to coat. Drain pickled vegetables and arrange on top of salad.