In a large pot, combine chicken thighs, garlic, ginger, and scallion whites. Season with salt and pepper. Pour in enough water to cover the chicken by about an inch. Bring to a boil over medium-high heat, then reduce to low and simmer for approximately 15 minutes.

While the soup base simmers, mix together black rice vinegar, soy sauce, and toasted sesame oil in a small bowl. Adjust seasoning to taste.

Remove the chicken from the pot, shred into bite-sized pieces, and return to the pot.

Add the dried ramen noodles and carrot matchsticks to the broth. Cook noodles according to package instructions, typically 3-4 minutes.

Stir to combine everything, allowing the soup to heat through for another minute.

Serve in bowls, garnishing with the greens of the scallions and a drizzle of the prepared sauce.