In a large pot (or dutch oven), saute the celery, onion and carrots in butter for about 5 minutes until the vegetables are crisp-tender.
Add cauliflower, chicken broth and water and bring to a boil.
Reduce heat, cover and simmer for about 20 minutes or until cauliflower is tender.
Let soup slightly cool and in batches add to a blender or food processor.
Blend until mixture is smooth and return to pot over medium heat.
In a bowl, whisk together flour and milk until smooth then add to pot.
Bring to a boil and stir until it begins to thicken.
Reduce heat and add half and half, parsley, salt, dill weed and white pepper.