Cut 1 English cucumber into very thin slices. Toss cucumber with 1 teaspoon kosher salt; let stand 15 minutes. Drain; firmly squeeze dry, and place in a bowl. Drizzle with 2 tablespoons seasoned rice vinegar and 3/4 teaspoon dark sesame oil; toss well. Stir in 2 teaspoons toasted sesame seeds.
Cook 8 ounces wide rice noodles according to package directions; drain and rinse with cold water. Combine noodles, 1/2 cup shaved carrots, 1/4 cup green onion strips, 2 tablespoons seasoned rice vinegar, 1 tablespoon dark sesame oil, 1/4 teaspoon crushed red pepper, and 1/4 teaspoon salt.