Place cauliflower blossoms, grated carrots, and chopped celery into a saucepan. Pour in water, add broth, bring to a boil and cook for 10-15 minutes until softened.
In another saucepan, melt the butter, add flour, salt, and pepper, stir until smooth. While cooking over low heat, gradually pour in the milk, stirring constantly, cook until thickened.
Add the grated cheese, cook, stirring occasionally, until it melts. Pour the cheese sauce over the vegetables, stir and serve.