Place the thinly sliced lemongrass in a small bowl, then pour ½ cup of boiling water over it and allow to steep for at least 10 minutes. Remove the lemongrass, reserving the water.
Puree the chilies, shallots, garlic, ginger, cilantro stems, coriander, turmeric, curry, and 2 tablespoons of the lemongrass water. Process until smooth, adding more lemongrass water if needed.
In a large pot over medium heat, warm the vegetable oil. Add the spicy curry puree and cook for 4-6 minutes, stirring constantly. Add the coconut milk and broth. Bring to a boil and add the chicken. Reduce the heat to a simmer and cook the chicken until fork-tender, about 10-15 minutes. Transfer the chicken to a plate, allow to cool slightly, then shred the meat.
Cook the noodles according to package directions. Add the fish sauce, sugar, and shredded chicken to the soup. Season with salt, if needed. Divide the soup and noodles among bowls and serve with the desired toppings.