Add broccoli, onion, carrot, garlic, salt, pepper, celery salt, and chicken stock to a Crock Pot. Cook on low for 6-8 hrs or on high for 3-4 hours.
Once done, use an immersion blender, blender, or Vitamix and blend soup until creamy. Return to Crock Pot on low.
In a small sauce pan on stovetop, heat butter over medium and sprinkle on flour. Whisk as butter melts to create a roux. Once all the butter is melted and flour incorporated, slowly add milk and whisk. Slowly add shredded cheese and whisk until well combined into a thick cheese sauce. Reserve 1/4-1/2 cup of cheese.
Add cheese sauce to soup and give a gentle mix. Add some of the reserved cheese and give another mix.
Serve in soup bowls and garnish with fresh parsley and some shredded cheese.