Prepare the Vegetables and Chicken: Heat the vegetable oil in a large pot over medium heat. Add the diced carrots and sliced green onions, sautéing until the vegetables begin to soften, about 4-5 minutes. Stir in the minced garlic and ginger, cooking for an additional minute until fragrant.

Prepare the Chicken: Season the chicken breasts with salt and freshly cracked pepper. Add them to the pot, cooking for about 5 minutes per side until golden brown but not fully cooked through.

Simmer the Broth: Pour the chicken broth into the pot, scraping up any browned bits from the bottom. Stir in the soy sauce, mirin, rice vinegar, Sriracha, sesame oil, and sugar. Bring the mixture to a boil, then reduce the heat and let it simmer for 10 minutes to allow the flavors to meld together.

Shred the Chicken: While the broth simmers, shred the partially cooked chicken into bite-sized pieces. Return the shredded chicken to the pot along with the chopped Napa cabbage and sliced mushrooms. Continue to simmer for another 5-7 minutes until the vegetables are tender and the chicken is cooked through.

Prepare the Noodles: In a different pot, boil the ramen noodles following the instructions on the package. Drain and set aside.

Assemble the Soup: Add the cooked ramen noodles to the soup pot, stirring gently to combine. Taste the soup and adjust seasoning as needed, adding more soy sauce or salt if desired.

Serve: Ladle the soup into bowls, garnishing with freshly chopped cilantro. Serve hot and enjoy this comforting, flavorful bowl of Asian Chicken Noodle Soup.