Combine broccoli stems and florets, chicken stock, water, smashed garlic, kosher salt, and black pepper in a large pot. Bring to a vigorous boil for about 5 minutes.

Reduce heat, cover the pot, and let the soup simmer gently for about 30 minutes.

Remove from heat and blend the soup slightly to maintain some broccoli texture.

Stir in the orzo or ditalini pasta and cook uncovered for about 15 minutes.

Taste and adjust seasoning with optional nutmeg, salt, and pepper.

Ladle hot soup into bowls, sprinkle with Parmesan cheese and drizzle with olive oil before serving.