Preheat the oven to 350 degrees F. Grease a 2-quart baking dish with butter or nonstick cooking spray.
In a bowl, mix the crushed crackers, Parmesan and melted butter. Place the broccoli in the baking dish.
In a pot, melt the remaining 3 tablespoons butter. Add the flour and stir together. Continue to stir while cooking for about 3 minutes. Whisk in the milk, stir to break up the flour, and heat the mixture to a soft boil, stirring constantly. Once the milk thickens, add the ketchup, Worcestershire, salt, sugar, pepper and cayenne. Add the cream cheese and blue cheese. Whisk until blended smoothly. Pour the cheese sauce over the broccoli. Pour the cracker mix over the casserole. Bake, uncovered, for 30 minutes.