Place broccoli stems and florets, chicken stock, water, smashed garlic, kosher salt, and freshly ground black pepper in a large pot or Dutch oven.
Heat the pot until the mixture begins to boil, then lower the heat, cover, and simmer gently for 30 minutes so the flavors meld.
After simmering, lightly crush the broccoli in the pot using a potato masher or pulse a few times with an immersion blender, leaving chunks for texture.
Add the orzo or ditalini pasta to the pot and cook uncovered, stirring regularly, for 15 minutes until the pasta softens and the soup thickens.
Mix in ground nutmeg if desired, then taste and adjust salt and pepper to your liking.
Serve the soup hot, garnished generously with grated parmesan, a drizzle of extra virgin olive oil, and a pinch of black pepper.
