In a large pot, combine the chicken thighs, sliced garlic, finely chopped ginger, scallion whites, kosher salt, freshly ground pepper, and enough water to cover all ingredients. Bring this mixture to a rolling boil over medium-high heat, stirring occasionally. Once boiling, reduce the heat and let it simmer uncovered for about 15 minutes, until the chicken is tender and cooked through.

While the chicken is simmering, take a small bowl and whisk together the black rice vinegar, soy sauce, and toasted sesame oil. Set this sauce aside.

Once the chicken is tender, remove it from the pot and place it on a cutting board to cool slightly. Add the dried ramen noodles and sliced carrots to the simmering broth. Cook according to the noodle package instructions, typically around 3 to 4 minutes.

As the noodles cook, shred the cooked chicken using two forks. Once the noodles are ready, return the shredded chicken to the pot, stirring gently to combine everything together. Taste the broth and adjust the seasoning as necessary.

Ladle the hot soup into bowls, making sure each bowl gets a portion of noodles, chicken, and broth. Top each serving with the reserved scallion greens and drizzle the prepared sauce over the soup.