In a large pot over medium-high heat, combine the chicken thighs, garlic, ginger, scallion whites, salt, pepper, and water. Bring to a rolling boil, then reduce heat and simmer uncovered for about 15 minutes.

While the chicken simmers, whisk together black rice vinegar, soy sauce, and toasted sesame oil in a medium bowl. Set this mixture aside.

Remove the cooked chicken from the pot and shred it. Return the shredded chicken to the pot.

Add the noodles and carrots to the pot, stir gently, and cook according to noodle package instructions, about 3-4 minutes.

Return the reserved chicken to the pot, stir gently for 1 minute, and adjust seasoning as needed.

Ladle soup into bowls, garnish with scallion greens, and drizzle with soy-vinegar sauce if desired.