Clean cauliflower and cut into pieces and place in a large saucepan. Add chicken broth to 1/2-inch covering cauliflower. Cover and simmer until tender (about 30 minutes). Remove about 1/2 cup cauliflower buds from liquid and set aside.
Cool remaining cauliflower and broth 10-15 minutes then purée the cauliflower in a food processor until smooth. Return purée to pot and add half and half, season to taste with salt and pepper and reheat. Mix parsley with reserved cauliflower and use to garnish each serving.