Combine the stock, kombu, shiitake, garlic, ginger, and scallion whites in a pot. Let the kombu soak in the cold stock for 20 minutes before turning on the heat.
Warm the pot over medium-low heat until small bubbles just begin to form around the edges, not a rolling boil. Hold it there for 30 minutes.
Remove the kombu before the broth gets any hotter than a bare simmer. Pull out the shiitake, slice them thinly, and set aside for topping. Discard the kombu.
Stir the soy sauce, rice vinegar, and sugar into the broth. Keep it warm over low heat while you sear the tuna.
Pat the tuna steaks completely dry with paper towels. Season all over with salt and pepper, pressing into sesame seeds now if using.
Heat the oil in a heavy skillet over high heat until it's just barely starting to smoke. Sear the tuna for 45 to 60 seconds per side.
Rest the tuna for 2 minutes, then slice into 1/2-inch pieces against the grain.
Cook the noodles according to the package directions and divide among four bowls.
Ladle the hot broth over the noodles. Top each bowl with sliced tuna, the reserved shiitake, napa cabbage, a soft-boiled egg half, scallion greens, and nori.