Cut rind off cheese. Combine rind, stock, garlic, parsley, and oil in a 3-quart pot, then simmer gently, partially covered, 30 minutes. Discard parsley and rind and season broth with salt.
Add tortellini and simmer, partially covered, until al dente, about 10 minutes. Add spinach and simmer, uncovered, 1 minute. Divide among 4 soup plates, then shave cheese over soup to taste.
