Blanch the broccoli by throwing florets into boiling water for 30 seconds, then draining and pouring into ice water. When cool, drain and set aside. Keep in the fridge to keep cool.
To make the sauce, melt the butter in a pot over medium heat and sprinkle in the flour. Whisk to combine and cook until thick, about 1 minute. Pour in the milk and heat until it thickens. Add the grated cheese, cream cheese, salt, Cajun spice, mustard powder and pepper to taste. Stir to melt. Taste and adjust seasonings. Serve hot with the cold broccoli and use as a dipping sauce.