Preheat the oven to 375F degrees.

Grease a 1 1/2 quart casserole dish and set aside.

Fill a 5 quart pot about 2/3rds full of water and bring to a boil. First add the butternut squash to the water and boil for 2 minutes. Then add the cauliflower and bring back to a boil and boil for 1 minute. 

Next add the broccoli, bring the water back to a boil and cook for 2 minutes. 

Drain vegetables and run under cold water to stop the cooking process. 

Place drained vegetables in the prepared baking dish and set aside. 

To make the cheese sauce, melt the butter in a saucepan over medium heat. Whisk in the flour and cook until nice and smooth {about 1 minute}. Gradually add in the milk, stirring until smooth and thickened. 

Stir in the mustard and pepper, then add about ¾ of each cheese into the pot, stirring until melted. 

Pour cheese sauce over the vegetables and sprinkle with the remaining shredded cheese and smoked paprika.

Bake for 20 – 25 minutes or until the cheese has browned a bit and the vegetables are warmed through.