Heat the oil in a soup pot over medium heat. Add the onion and cook, stirring, until softened and translucent, about 4 minutes. Add the garlic and nutmeg and cook for 30 seconds. Add the broccoli and chicken broth and bring the mixture to a boil. Reduce the heat to medium-low and cook until the broccoli is tender, about 5 minutes. Remove from the heat and allow to cool slightly, about 15 minutes.
Meanwhile, in a small saucepan, whisk together the milk and flour until the flour dissolves. Heat the mixture over medium-high heat, stirring constantly, and bring to a gentle boil. Reduce the heat to medium-low and cook, stirring occasionally, until the mixture has thickened, about 3 minutes. Add one cup of the cheese and cook, stirring, until melted, 2 minutes more. Remove from the heat and cover to keep warm.
Working with about 1 cup at a time, puree the broccoli mixture in a blender until it is mostly smooth but still has some chunks, and then transfer it to another pot. (Alternatively, you can use an immersion blender.) Stir the cheese mixture into the broccoli puree, season with salt and black pepper to taste, and cook over medium-low heat until warmed through, 3 to 5 minutes more. Serve garnished with the remaining cheese.
Reprinted with permission from Comfort Food Fix by Ellie Krieger, copyright (c) 2011. Published by Wiley.