Heat 3 tablespoons vegetable oil in a large skillet over medium heat. Add the garlic, onion and ginger and cook, stirring occasionally, until the onion is dark brown, about 30 minutes.
Meanwhile, make the broth: Put the bacon and chicken wings in a Dutch oven and add enough water to cover. Bring to a boil, then reduce the heat to medium and simmer 10 minutes. Drain and wipe the pot clean. Rinse the bacon and wings under cold water, then return to the pot; add 4 quarts water and the dried mushrooms. Bring to a boil, then reduce the heat to medium; add the garlic mixture and gently simmer 1 hour, 15 minutes.
Strain the broth through a colander into a large bowl, pressing on the solids to extract as much of the liquid as possible. Skim any excess fat from the surface. Measure the broth, adding water if necessary to yield 2 quarts. (The broth can be made up to 4 days ahead; cover and refrigerate.)
Just before serving, heat the remaining 1 tablespoon vegetable oil and the scallions in a medium skillet over medium heat until the mixture starts sizzling. Add the sake, soy sauce, 1 1/2 teaspoons salt, the sugar, peppercorns and 1/2 cup water. Simmer, reducing to 1/2 cup, about 5 minutes.
Bring the broth and the scallion mixture to a simmer in a large saucepan over medium heat. Add the noodles and cook until softened, 1 to 3 minutes. Gently pull the noodles apart with tongs. Transfer the soup to bowls and top as desired.
Take your pick: These taste great in just about any combination.
Shredded rotisserie chicken
Nori strips (seaweed)
Cubed firm tofu
Toasted sesame seeds
Roasted squash: Toss cubed butternut or kabocha squash (no need to peel) with olive oil and sprinkle with salt, sugar and red pepper flakes. Roast at 425 degrees F, 30 minutes.
Sauteed shrimp: Stir-fry peeled deveined shrimp in hot olive oil with minced ginger, chopped scallions and a pinch each of sugar, salt and pepper.
Roasted pork belly: Put 1 cup each sake and water, 1/2 cup each soy sauce and mirin, and 1/4 cup sugar in a Dutch oven. Add 2 pounds skinless pork belly, 1 quartered onion, 1/2 head garlic and 4 thin slices ginger. Cover with foil. Roast at 325 degrees F,3 hours; slice.