Gradually stir in chicken broth, stirring constantly to avoid lumps. When smooth, slowly add the 1-1/2 cups of water, continuing to stir.
Add cauliflower pieces and heat to a very light simmer. Cover and turn heat to LOW, to a bare simmer, until cauliflower is very tender, at least 20 minutes. Stir FREQUENTLY.
When cauliflower is very tender and mushy, add the milk and stir it in well. Bring entire mixture back up to temperature, but do not boil or allow milk to scorch.