Combine water, spareribs, 1/2 of the onion, and 3 cloves garlic in a pot over high heat. Bring to a boil, reduce heat, and simmer until meat easily falls off the bones, about 2 hours.

Remove bones from spareribs and return meat to the broth. Add chicken broth and bring to a boil. Stir in mustard greens, lime juice, jalapenos, fish sauce, and remaining onion and garlic. Boil for 5 minutes. Stir in cilantro and season with salt.