Preheat oven to 400°. Combine first 3 ingredients in a 13 x 9-inch baking pan; toss to coat. Bake for 30 minutes. Remove ribs from pan, and set aside. Add 1/2 cup water to pan, and stir to deglaze pan.
Combine the pan drippings, ribs, remaining 12 cups water, peppercorns, onions, green onions, and carrots in a large Dutch oven or stockpot; bring to a boil. Reduce heat, and simmer, uncovered, 2 hours.
Remove ribs from broth, and let cool completely. Remove meat from bones; discard bones, fat, and gristle. Place meat in a bowl; cover and chill. Strain broth through a sieve into a large bowl; discard solids. Cover broth, and chill 12 hours. Skim solidified fat from surface of broth, and discard.
Combine broth, meat, mushrooms, tofu, 3 tablespoons soy sauce, and salt in Dutch oven; bring to a simmer. Cover and cook 10 minutes. Spoon noodles into individual soup bowls. Ladle soup into each bowl, and sprinkle with sliced green onions and cilantro.