Step 1

Roast the chicken wings: Arrange a rack in the middle of the oven and heat 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 mix well, then roast for another 20 minutes.

Step 2

Deglaze the roasting pan: Transfer the chicken and vegetables from the roasting pan to a large 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 wooden spoon, scrape up all the flavorful browned bits from the bottom of the pan. Bring to a boil, then carefully pour everything into the stockpot.

Step 3

Add the aromatics and water: Add the garlic, ginger, shiitakes, kombu, and remaining 8 cups of water and mix well. Bring the mixture just to a simmer (a few bubbles around the edges) over high heat.

Step 4

Simmer the broth: Reduce the heat as low as your stove will allow, add the tamari or soy sauce, and simmer, 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 and discard the solids. Refrigerate the broth overnight. Before using, skim the solidified fat off the surface and discard.