Preheat oven to 350°F. Spray a 9x13-inch baking dish with nonstick cooking spray. Scatter broccoli florets evenly over bottom of dish. Scatter chicken over broccoli. Set aside.
Heat Cauliflower Purée in a saucepan set over medium heat. Add milk or cream to thin to spreading consistency, if too thick. Season with Creole seasoning. Pour purée evenly over chicken and broccoli.
Scatter the shredded cheese evenly over casserole. Scatter breadcrumbs evenly over cheese. Bake until browned and bubbling, about 30 minutes.

Cauliflower Purée
Add cauliflower to a large pot, preferably a Dutch oven, and add enough water to cover. Set over high heat and bring to a boil. Cook until cauliflower is fork-tender, about 12 minutes. Drain thoroughly. Return cauliflower to pot. Add butter and blend. Add half the milk or cream and blend. Purée with an immersion blender or in a traditional blender. Add more milk or cream, blending constantly, until desired texture is reached.

Season with salt and pepper and serve.