In a large stockpot, bring plenty of salted water to the boil. Once the water has reached a rolling boil, add 4 cups of cauliflower florets to the pot; cover and let the cauliflower cook for 2 minutes, then add the broccoli and continue cooking for a further 2 minutes.
Promplty drain the cauliflower and broccoli and place them in a large bowl; run some cold water over them until the water in the bowl remains cold and the vegetables feel cold to the touch. This will halt the cooking process and also seal in the flavor and color of the vegetables. Drain well and set aside.
Preheat your oven to 350°F; Melt the fat in a medium saucepan set over medium heat; add the onion, salt and pepper and cook until the onion starts to color and become fragrant, about 3 minutes.
Add the remaining 4 cups of cauliflower florets and continue cooking for 2 minutes, then pour in the bone broth and bring it to the boil; lower the heat, cover and simmer until the cauliflower is super tender and even slightly overcooked, about 8 to 10 minutes.
Carefully pour this mixture into the container of your high-speed blender; add milk, Dijon mustard, grated sharp cheddar and parmesan cheese and process until smooth and creamy.
Pour this sauce over the blanched cauliflower and broccoli and toss to coat; transfer to a 9" baking dish, top with grated mozzarella and remaining grated sharp cheddar cheese. Bake for 30-35 minutes or until the cheese on top is golden and sauce bubbles on the sides.