Peel and cut carrot in half. Use mandoline to create ribbons with one half and set aside. Chop other half of carrot for broth.
In large pot, heat 1 tbsp olive oil over medium heat. Add chives, garlic, lemongrass, ginger, chopped carrot and celery; cook, stirring until tender, about 5 minutes. Add 6 cups water, dried shiitakes, kaffir leaves, soy sauce and nuoc cham sauce. Bring to boil; reduce heat and simmer for 1 hour. Season with salt and pepper.
In large bowl, stir together lemongrass, ginger, chives, garlic and chili. Finely chop three-quarters of the shrimp; add to bowl with cornstarch and stir to combine. Chop remaining shrimp into large pieces.
With wet hands, divide shrimp mixture into 16 even portions and gently roll into balls.
Strain broth through a fine sieve. Pour back into pot and season with salt and pepper, if necessary. Bring to a boil; add fresh shiitakes and cook on medium-high until mushrooms are tender, about 10 minutes. Add reserved carrot ribbons and meatballs, and poach over medium heat for 5 minutes.
Serve meatballs with broth.