Step 1

Heat oil in a large pot over medium heat. Add onion and garlic and cook, stirring occasionally, until softened, 2 to 3 minutes. Add ginger; cook, stirring, for 1 minute. Add broth and chicken. Cover, increase heat to high and bring to a simmer. Uncover and cook, turning the chicken occasionally, until an instant-read thermometer inserted into the thickest part without touching bone registers 165 degrees F, 20 to 22 minutes. Skim any foam from the surface as the chicken cooks. Transfer the chicken to a clean cutting board. When cool enough to handle, remove the meat from the bones and shred.

Step 2

Meanwhile, add cabbage, mushrooms and carrots to the pot; return to a simmer. Cook until vegetables are tender, 4 to 10 minutes. Stir in the shredded chicken, salt, pepper and noodles and cook until heated through, about 3 minutes more. Remove from heat and stir in miso.