Combine 1⁄2 cup of the broth with the salt, sugar, chile sauce, vinegar and soy sauce. Set this sauce mixture near the stove.
Put the oil and the garlic in a small saucepan. Heat over medium-low heat until the garlic sizzles and is light blond, 3 to 4 minutes. Remove the pan from heat for about 15 seconds to cool slightly, then add the sauce mixture. Place the pan over high heat and bring to a boil. Stir the cornstarch slurry, then swirl into the bubbly sauce. Once thickened, about 15 seconds, remove from heat and set aside for at least 10 minutes before using. This makes about 1/2 cup sauce.
Meanwhile, boil the noodles in a pot of water until tender chewy following the package instructions, about 5 to 7 minutes. Drain, cool quickly under running water, then set aside to fully drain and cool.
Reheat the remaining broth in a saucepan over medium heat. Meanwhile, cut or shred the chicken into bite-size pieces and, if needed, warm in a microwave oven to remove the chill and refresh; ideally the chicken has some succulence. Set aside.
To assemble, have 4 rice bowls for broth and 4 noodle-soup-size bowls for the salad. Put a little green onion into each rice bowl (use the rest for the noodle salad). Set near the broth.
Divide the lettuce among the noodle soup bowls. Add a portion of noodles and chicken, then drizzle over the sauce to taste. Top with the remaining green onion, cilantro, mint (or basil), peanut, and fried shallots (or onion).
Ladle the hot broth into the rice bowls. Serve immediately with the noodle salad bowls. Invite guests to wield spoons and chopsticks to toss their salads and enjoy the broth as soothing interludes. If the noodles seem too heavy with sauce, mix in a spoonful of broth.