In a large dutch oven or soup stock pot, melt butter over low heat. Add the onion and simmer until slightly translucent, about 10 minutes. Add the garlic and stir for 1-2 more minutes, until fragrant.

Sprinkle the flour over the buttery onions and whisk together for 1 more minute.

Increase heat to medium. While whisking, slowly pour the chicken broth into the flour mixture, stopping once or twice so the mixture is well combined. Continue whisking while pouring the heavy cream and water. Whisk until a creamy (no-lump) consistency is achieved.

Add celery, carrots, broccoli, and cauliflower to the soup and stir. Season the soup with salt, pepper, paprika, and dijon mustard. Bring to a boil on medium heat. Once boiling hot, reduce to simmer on low. Cook for 15-20 minutes, until the vegetables, especially carrots, are fork tender.

Once the vegetables are cooked to your liking, turn off heat. Slowly, add the grated cheddar cheese while stirring continuously to melt it in to the soup. Adjust soup seasonings as desired, adding more salt and pepper if needed.

If you prefer your soup to not have any large vegetables, you can puree it in a blender or use an immersion blender to achieve your desired consistency. I like this soup to not be thick, so I leave mine the way it is.