If you’re starting with a leftover rotisserie chicken carcass, scavenge it for good meaty bits, and set them aside. If you have purchased a cooked chicken expressly for this recipe, then carefully cut away the breast meat, reserve the drumsticks, and use your fingers to shred off the leg meat—but just the big, fit-for-a-king pieces that come away easily. You can leave plenty of chicken on the carcass; that clingy meat will make for a flavorful soup. Pull or slice the meat into bite-size pieces and reserve in the fridge while you make the broth
Break the chicken carcass into a few pieces and put them in a stockpot. Trim the roots and dark green parts of the scallions and add them to the pot; thinly slice the white and tender green parts and reserve them to garnish the soup. Add the ginger, carrot (if using), shiitake, and bacon. Add the water and bring to a boil. Reduce the heat from a rolling boil to a rollicking simmer, and skim any froth that collects on the surface during the first 10 minutes of simmering.
Cook until the liquid is reduced by one-third (to 8 cups), about 2 hours. Strain the broth. (That shiitake is probably pretty delicious and tender at this point so you can save and slice it and use it as a garnish on the finished dish, but scrap the rest.) The broth can be used immediately or refrigerated for up to 2 days.
To serve: Bring the broth to a strong simmer and cook the ramen noodles according to package directions. Drain the noodles very well, and portion them out among 4 deep soup bowls. Top with broth. Season each bowl with 2 teaspoons soy sauce, a portion of the reserved chicken meat, scallions, half an egg, and whatever else you’ve got. (See ideas on the following pages!) Eat immediately.