1In a medium-sized cooking pot, add water and broccoli florets and bring to boil; reduce heat and cook for about 3 minutes. Drain, reserving all of the water.
2In a food processor or blender, process half the cooked broccoli until fairly smooth. Chop remaining broccoli and set aside.
3In a heavy-bottomed cooking pot, melt butter or margarine, add onion and celery and cook for about 3 to 4 minutes until soft. Stir in flour; cook, stirring constantly for about 1 to 2 minutes. Add reserved water and chicken bouillon granules, and bring to boil, stirring constantly. Reduce heat to medium; simmer, stirring constantly until thickened.
4Stir in milk, nutmeg, pepper, and processed and chopped broccoli, and heat through. Adjust seasonings to taste. Serve garnished with grated cheddar cheese.