I used to cook the broccoli first and then chop it and add it to the soup but I was rushed for time one day and just made the soup base, threw the chopped broccoli in and simmered it. It tasted the same and I was able to omit a step.
You can also stir in a cup or more of shredded cheddar cheese at the end for a broccoli-cheese soup.
Rinse the broccoli, peel the stalks, cut the woody ends off and chop, leaving some florets a little larger than others. Set aside.
Melt 1/2 stick of the butter in a saucepot, add the onions, a litle salt and pepper and saute over medium heat until translucent. Add the other half stick of butter and when melted add the flour, stir in and saute over medium heat a few minutes.
Stir in the milk, water, chicken base and bring to a boil over medium heat, stirring constantly.(Or you can use 4 cups of chicken broth instead of the chicken base & water.) Add the uncooked broccoli, the dash of nutmeg and bring back to a boil, stirring. Reduce heat to low and simmer uncovered about 10 minutes.
Using an immersion blender (or a potato masher), lightly blend so some of the broccoli is pureed, leaving some whole pieces. Serve with a sprinkle of shredded cheddar cheese.
NOTE: You can make a broccoli-cheddar cheese soup by stirring 1 cup of shredded cheddar at the end of the cooking time.