Melt butter, coconut oil and arrowroot in a heavy-bottomed pot on medium-low. Add onion, mushrooms, celery, red pepper, tomatoes, celery seed, sea salt and Old Bay. Cook until onions are tender and translucent.
Add broth, water, cauliflower, and dill. Bring to boil. Reduce heat to a simmer. Simmer for 30 minutes. Season with salt and pepper to taste.
Using an immersion blender, blend pot ingredients until smooth. (An alternative is to transfer small batches to a stand blender, and blend until smooth).