In a large pot, combine the chicken thighs, garlic, ginger, the white parts of scallions, kosher salt, and pepper. Pour in water and bring to a gentle boil.

Once boiling, reduce heat to medium-low and let the soup simmer uncovered for about 15 minutes.

While the chicken is cooking, whisk together black rice vinegar, soy sauce, and toasted sesame oil in a small bowl. Add crispy chili oil if desired.

After 15 minutes, remove the chicken, shred into bite-sized pieces, return to the pot, and add the noodles and carrots. Cook noodles per package instructions.

Once noodles are cooked, stir everything together and adjust seasoning as needed.

Ladle soup into bowls and garnish with reserved scallion greens. Drizzle soy-vinegar sauce before serving.