Bring the chicken, garlic, ginger, scallion whites, salt, pepper, and water to a boil in a 4-to-5-quart pot. Reduce the heat to medium-low, and simmer, uncovered, stirring occasionally, until the chicken is very tender and cooked through, about 15 minutes.

While the soup simmers, whisk together the vinegar, soy sauce, and sesame oil in a bowl, and add as much or as little chili crisp as your heart desires.

Remove the chicken with tongs, and transfer it to a cutting board. Add the noodles and carrot to the broth, following the cooking-time estimation on your noodles’ package directions. Use two forks to shred the chicken into bite-sized pieces.

Once the noodles are done, return the chicken to the pot, and rewarm for 1 minute. Taste, adjusting seasoning if needed.

Divide the soup between bowls. Add a handful of scallion greens and drizzle each bowl with 1 tablespoon of the soy sauce mixture, adding more to taste.