Place the broccoli stems and florets, chicken stock, water, smashed garlic cloves, kosher salt, and freshly ground black pepper into a large pot or Dutch oven.
Turn the heat to high and bring everything to a boil, then lower the heat, cover the pot, and let it simmer gently for 30 minutes to blend the flavors.
After simmering, press down on the broccoli with a potato masher directly in the pot to break it up, or carefully pulse with an immersion blender, keeping some chunks for texture.
Add the orzo or ditalini pasta into the soup and leave it uncovered while cooking for 15 minutes, stirring regularly to stop the pasta from sticking.
Stir in ground nutmeg if desired, then check and adjust the seasoning with more salt and pepper as needed.
Serve the soup hot in bowls, topping each with a generous amount of finely grated parmesan and a drizzle of extra virgin olive oil for richness.
