Place dried scallops and dried mushrooms in a bowl; pour in hot water to cover and let stand to rehydrate, about 10 minutes. Rinse and drain rice; set aside.
Separate any meat from bones of turkey carcass; set aside. Place bones and 9 cups hot water in a large stockpot and bring to a boil. Drain mushrooms and scallops; squeeze out any excess water. Break scallops into smaller pieces; slice mushrooms thinly.
Stir scallops, mushrooms, rice, and turkey meat into the stockpot; reduce heat to allow congee to simmer, partially covered, stirring occasionally for a smooth congee, until rice is tender and congee is thick, about 2 hours. If you like a thinner congee, stir in hot water a few tablespoons at a time.
Ladle congee into individual bowls; top each bowl with cilantro, green onions, ginger, peanuts, red onion, sesame oil, and white pepper as desired.
