Heat the oil in a large pot over medium heat. Add the ginger, garlic, shallot, and chili pepper, if using. Cook, stirring, until the shallot is softened, about 4 minutes.

Add the miso paste and cook, stirring, until it is slightly darkened, about 2 minutes.

Slowly add the broth and scrape up any browned bits on the bottom of the pot. Add the chicken and bring to a simmer over high heat. Reduce the heat to low, cover, and let simmer for 10-15 minutes, until the chicken is cooked through and registers at least 165°F on an instant-read thermometer.

Meanwhile, bring a large pot of salted water to a boil. Cook the noodles according to package instructions. Drain and set aside.

Soft-boil the eggs***: Fill a large bowl with water and ice to create an ice bath. Bring a medium pot of water to a boil. With a slotted spoon, gently lower in the eggs and return to a high simmer. Reduce the heat to maintain a simmer (not a hard boil) and cook for 6 minutes. Immediately transfer the eggs to the ice bath. Let chill for 2 minutes, then remove, peel, and slice in half.

When the chicken is cooked, transfer it to a bowl. Shred the meat with two forks, discarding the skin and bones. Return the meat to the pot.

If using, add the frozen vegetables to the pot, stir, and let heat through for a few minutes.

To serve, divide the noodles between bowls. Ladle on the soup. Top with the soft-boiled eggs and any other desired toppings.