Step 1

Roast the chicken wings. Arrange a rack in the middle of the oven and heat the oven to 425°F. Place the chicken wings in a stovetop-safe roasting pan or casserole dish and roast until well-browned, about 30 minutes. Reduce the heat to 375°F, add the carrots and scallions, and stir to combine. Roast for 20 minutes more.

Step 2

Deglaze the roasting pan. Transfer the chicken and vegetables to a stockpot. Place the now-empty roasting pan on the stovetop over high heat. Add 2 cups of the water and, stirring and scraping vigorously with a heatproof or metal spoon, scrape up all the flavorful browned bits from the bottom of the pan. Bring to a boil, then carefully pour the mixture into the stockpot.

Step 3

Amp up the aromatics. Add the garlic, ginger, shiitakes, kombu, and remaining 8 cups water to the pot and stir to combine. Bring just to a simmer over high heat — just a few bubbles around the edges.

Step 4

Simmer the broth. Reduce the heat as low as your stove will allow, add the soy sauce, and simmer uncovered, occasionally skimming the fat and scum that accumulates on the surface, until the chicken has fallen completely off the bone and the wing bones come apart easily, 3 to 3 1/2 hours.

Step 5

Strain the broth. Pour the broth through a fine-mesh strainer into a large bowl; discard the solids. Cool the broth to room temperature, then cover and refrigerate overnight. Before using, skim the fat off the surface and discard.

Step 6

Make the tare. Combine the soy sauce and mirin in a small airtight container, seal, and refrigerate until ready to use.

Step 7

Cook the eggs. Fill a large saucepan with a few inches of water and place over high heat until it comes to a rolling boil. Reduce the heat so that the water is at a rapid simmer. Gently lower the eggs into the water 1 at a time, then simmer for 6 minutes. Remove the eggs with a slotted spoon to an ice water bath. Peel the cooled eggs, cut in half lengthwise, and set aside.

Step 8

Cook the noodles. Return the egg cooking water to a boil, add the noodles, and cook according to package directions, 3 to 5 minutes. Drain the noodles and run under cool water to stop the cooking.

Step 9

Simmer and flavor the broth. Bring the broth back to a boil in a separate saucepan. Remove from the heat and add the tare to taste.

Step 10

Assemble the bowls. Divide the noodles between 4 deep, wide bowls (or more bowls if you want to have smaller servings). Ladle on the hot broth. Top each bowl with 1 to 2 egg halves, bamboo shoots, scallions, and nori and drizzle with oil.