In a large soup pot, combine chopped broccoli stems and florets, chicken stock, water, minced garlic, kosher salt, and freshly ground black pepper. Stir everything together to ensure the broccoli is submerged. Turn the heat to medium-high and bring the mixture to a gentle boil, which should take about 5 minutes.

Once boiling, reduce the heat to low, cover the pot with a lid, and let it simmer for 30 minutes.

After 30 minutes, remove the pot from the heat. Using an immersion blender, carefully blend the soup until it reaches your desired consistency—chunky or smooth.

Return the blended soup to low heat and stir in orzo pasta. Cook uncovered for about 15 minutes, stirring often to prevent sticking.

Once the orzo has cooked, add ground nutmeg if desired, then taste the soup and adjust seasoning with extra salt and pepper as needed.