Preparation Bring chicken carcass, shiitake stems, garlic, 1 tsp. salt, and 8 cups water to a boil in a large pot, skimming foam from surface as needed. Cover pot and reduce heat to medium. Simmer 15 minutes. Strain broth through a fine-mesh sieve into a large bowl. Rinse out pot, then pour broth back in. Meanwhile, heat oil in a large skillet over medium-high. Cook mushroom caps, stirring occasionally, until golden brown and softened, 7–9 minutes. Transfer mushrooms to a plate; season with salt. Add cabbage to same skillet, press into an even layer, and cook, undisturbed, 2 minutes; season with salt. Turn cabbage with tongs, then continue to cook, undisturbed, until lightly charred and tender in some spots and still crisp in others, about 2 minutes. Add mushrooms, cabbage, and shredded chicken to broth and cook over medium heat just until chicken is warmed through, about 3 minutes. Season soup with salt and pepper. Divide among bowls and drizzle with chili oil if desired.
Preparation Bring chicken carcass, shiitake stems, garlic, 1 tsp. salt, and 8 cups water to a boil in a large pot, skimming foam from surface as needed. Cover pot and reduce heat to medium. Simmer 15 minutes. Strain broth through a fine-mesh sieve into a large bowl. Rinse out pot, then pour broth back in. Meanwhile, heat oil in a large skillet over medium-high. Cook mushroom caps, stirring occasionally, until golden brown and softened, 7–9 minutes. Transfer mushrooms to a plate; season with salt. Add cabbage to same skillet, press into an even layer, and cook, undisturbed, 2 minutes; season with salt. Turn cabbage with tongs, then continue to cook, undisturbed, until lightly charred and tender in some spots and still crisp in others, about 2 minutes. Add mushrooms, cabbage, and shredded chicken to broth and cook over medium heat just until chicken is warmed through, about 3 minutes. Season soup with salt and pepper. Divide among bowls and drizzle with chili oil if desired.