Mince the lower 2/3 of lemongrass stalk. Bruise the remaining upper portion of lemongrass stalk by hitting it with the back of a knife.

Pour chicken stock into a large pot; add minced lemongrass, bruised lemongrass stalk, 1/2 the ginger, lime leaves, garlic, and Sriracha sauce. Bring to a boil, reduce heat, and simmer. Add chicken to simmering broth; cook until chicken is no longer pink in the center, about 10 minutes. Remove lemongrass stalk and lime leaves using a slotted spoon; discard.

Place cilantro bundle in the broth and simmer for 2 minutes. Add coconut milk, remaining ginger, brown sugar, lime juice, and fish sauce. Remove cilantro bundle using a slotted spoon; discard. Simmer broth, 5 to 10 minutes.

Fill a large pot with water and bring to a rolling boil. Add ramen and cook until softened, about 3 minutes. Drain and portion noodles into serving bowls.

Mix carrots, tomatoes, and green onions into broth. Ladle broth over noodles; garnish with cilantro.