For dressing: Whisk together white miso paste, sesame oil, rice vinegar, and 1/4 cup olive oil. Drizzle 2 tablespoons dressing over drained albacore tuna. Stir in sesame seeds.
Cook sugar snap peas and carrots in salted boiling water 1 minute; plunge into cold water. Coarsely crush ramen noodles (discard seasoning packet).
Combine noodles, 6 cups chopped napa cabbage, basil, green onions, and 1/2 cup dressing. Top with tuna, snap peas and carrots, and soft-cooked eggs. Pass with remaining dressing and crushed red pepper.