Begin by cooking the chicken: Pat the chicken dry and season with the salt and pepper. In a Dutch oven on medium heat the oil and cook the breasts until golden on both sides, about four minutes. Remove the chicken to a plate. Add the garlic, ginger, and lemongrass and cook a minute. Add the chicken stock, carrots, soy sauce, fish sauce and and sugar and bring to a simmer. Add the chicken back to the pot and cover and simmer for 10 minutes, or until the chicken is fully cooked.
While the chicken cooks bring an inch of water to a boil in a three quart saucepan. Add the asparagus and squash and simmer covered for four minutes. Drain.
Boil the rice noodles according to the package directions
Remove the lemongrass and shred the chicken with two forks.
To serve the soup, place some shredded chicken, vegetables, and noodles in each bowl, and then pour the soup on top. Garnish each bowl with lime wedges, scallions, and cilantro.