1Wash, trim and coarsely chop the broccoli crowns and place in stock pot.
2Saute onion, garlic, celery seed, salt and pepper in pan with olive oil until transparent.
3Add onion mixture to stock pot and fill pan with water to cover. Simmer until broccoli is fork tender. Remove about 1 cup of broccoli and set aside.
4In SMALL* batches in blender or food processor, puree broccoli mixture along with stock. Place each completed batch into large bowl to hold until the everything has been pureed.
Toward the end of the batches, if the pureed mixture looks too watery, strain the remainder of the stock, saving the vegetables and enough water to cover the vegetables. Discard the remainder of the liquid (or if enough is left, freeze for another batch of soup, etc.).
5Return pureed mixture to stock pan. Cut up the remaining cup of broccoli that was set aside into smaller pieces and add to mixture in stock pan
6Add half & half and cheese. Heat, stirring occasionally, until cheese has melted. Do not boil.
7*NOTE: When processing hot foods in a blender or food processor, they will "explode". To be safe, make sure not to fill the container more than 1/3 full.