Heat oil in a large stockpot over medium-low heat. Add garlic; cook 10 seconds or until fragrant. Add broth, chicken, Parmesan cube, salt, pepper, and nutmeg. Bring to a boil; reduce heat to medium, and simmer 10 minutes. Remove chicken; set aside. Remove Parmesan cube; discard.
Return broth mixture to a boil. Add pasta; simmer 9 minutes or until pasta is tender.
Cut chicken-breast halves into thin strips; return to soup. Stir in spinach, and simmer 1 minute or until wilted. Divide soup evenly among 4 bowls; sprinkle with 1/4 cup shaved Parmesan cheese.