Saute the diced onion in the butter in a small frying pan on the stove top until the onion has turned translucent.
While the onion is cooking wash and trim the broccoli heads, trimming off as much of the woody stem as possible.
Line a 6 quart or larger slow cooker with a slow cooker liner (optional but makes clean up easier). Pour in the condensed cheddar cheese soup, cream of celery soup and then add your broccoli florets.
Add the evaporated milk, onions and spices and stir everything together well.
Cover and cook on LOW to 3 to 4 hours stirring at least once in the middle of the cooking time.
During the last 20 minutes of cooking, add the cooked rice and shredded cheese to the crock-pot and stir everything together and cook for 20 minutes to give the cheese some time to melt into the soup.
Serve in bowls with crusty bread to dip into your soup and enjoy!