Cook the noodles, rinse with cold water to stop the cooking. Set aside.
Use the back of a knife and lightly smash lemongrass and ginger. Trim the lemongrass into 4 inch pieces. Bring the lemongrass, ginger, lime leaves and broth to a boil in a large soup pot over medium high heat. Reduce the heat and simmer until flavors are combined, 8–10 minutes. Strain the broth and throw away the solids.
Add the chicken and return soup to a boil. Reduce heat, add mushrooms, red bell pepper and broccoli, bring to a simmer. Cook until the chicken is cooked through and mushrooms are soft, 20–25 minutes. Use a strainer if necessary. Mix in coconut milk, lime juice, fish sauce, and sugar.
Taste the soup & make adjustments according to taste. If you like it sweeter, add more sugar. Spicy, add chili oil. Saltier/brinier add more fish sauce. Creamier, more coconut milk.
Divide the noodles and soup among bowls. Serve with chili oil, cilantro, and lime wedges.
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