Start the recipe by soft boiling the eggs so they have time to marinate in the refrigerator for 5 to 12 hours. Bring a pot of water to 190 degrees, poke the large end of the eggs with a tack to release any air bubble that might be inside, and gently lower into the water. Maintain 190 degrees for 6.5 minutes and use a slotted spoon to move the eggs to an ice bath to stop the cooking process. Once they have cooled enough to handle, peel the eggs.
Mix the egg marinade ingredients in a shallow bowl. Add the eggs, making sure the marinade covers or barely floats the boiled eggs. Fold a paper towel into quarter size and use it to cover the eggs. Gently push the paper towel down into the marinade until it is soaked so that no portion of the egg goes without contacting the marinade. Refrigerate a minimum of 6 hours and up to 12.
Peel the eggs and place in a bowl of marinade, covering with a folded paper towel to keep all sides exposed to marinade.
Once your eggs have marinated, rub the inside loin with salt and pepper, then grill for 6 to 8 minutes or until they reach medium rare. Move the tenderloin to a warm plate and cover with foil to rest.
Slice the grilled tenderloin against the grain for maximum tenderness.
As the tenderloin grills, add the stock and bone broth to a large pot and bring to a simmer. Add the garlic, ginger, mushrooms, kombu sheet, soy sauce and white miso paste. Simmer for 20 minutes.
While the stock is simmering, bring 2 quarts of water to boil in a separate pot. Add 3 tablespoons of salt. Boil five bundles of Udon noodles and boil for 3 to 5 minutes. Drain and rinse under cool water to stop the cooking process.
The marinated eggs should have a soft, slightly runny, yolk.
To plate, add a serving of noodles to a large bowl. Spoon over broth to nearly fill bowl. Slice a marinated egg in half and gently place in bowl. Add several thin slices of tenderloin, the green onion, several thin slices of kombu, some diced bamboo, a bit of torn Swiss chard leaves, and two slices of narutomaki. Drizzle over some sesame oil.