1 — Gently poach the chicken and aromatics
Place the chicken thighs in a 4–5 qt pot with the sliced garlic, chopped ginger, and the white parts of the scallions. Add the kosher salt, a few grinds of pepper, and 10 cups of water. Bring to a boil over high heat, then lower to a medium-low simmer. Cook uncovered, stirring now and then, until the chicken is very tender — roughly 15 minutes.

2 — Whisk the finishing sauce
While the chicken simmers, combine the black rice vinegar, soy sauce, and toasted sesame oil in a small bowl. Stir in crispy chili oil to your preferred heat level. Set the sauce aside; you’ll use it to finish each bowl.

3 — Shred chicken; add noodles and carrots
Remove the cooked thighs from the pot with tongs and set them on a cutting board. Add the dried noodles and carrot matchsticks to the simmering broth and cook according to the noodle package (generally 3–4 minutes) until tender. Meanwhile, shred the chicken with two forks into bite-size pieces.

4 — Reunite and season
Return the shredded chicken to the pot, stir gently, and warm everything together for about 1 minute. Taste and adjust seasoning with salt or pepper, and add a splash of soy sauce if you want more umami.

5 — Serve with scallion greens and drizzle
Ladle the hot soup into bowls over the noodles and chicken. Top each portion with a generous handful of the reserved scallion greens for freshness. Spoon about 1 tablespoon of the soy-vinegar sauce over each bowl (more if desired) and offer extra chili oil at the table.