In a 5- to 6-quart pan, combine carrots, broth, seasoning seed, 1/4 teaspoon of the thyme, and 3 teaspoons of the ginger. Bring to boiling on high heat; cover and simmer 10 minutes.
Meanwhile, mix remaining 1/4 teaspoon ginger with beef, flour, and water. Shape into balls about 1 inch wide.
When carrots have cooked 10 minutes, drop meatballs into soup, then add bulgur. Return to a boil; simmer, covered for 10 minutes.
Stir cilantro into soup. Ladle soup into bowls and add to taste juice from lime wedges and salt.