Preheat oven to 350 and grease a 9x13x2 casserole dish. Add shredded chicken to the dish and set aside.
Heat a large saucepan to medium heat and add olive oil. When oil moves quickly around the pan, add onions and shallots. Cook, stirring every minute or so, until softened and translucent, approximately 6-8 minutes. Add garlic and cook, stirring constantly, another 30 seconds. Turn off heat, stir in ΒΌ cup water and keep pan on the warm burner.
Place half (6 ounces) of your frozen cauliflower rice in a microwave-safe dish and microwave 2 minutes, or until completely thawed. Add to a blender, along with yogurt, cream cheese, coconut milk, salt, pepper, onion powder and paprika. Scrape cooked onion mixture into the blender as well, and puree until smooth and creamy.
To your casserole dish, add 1 cup grated cheese, broccoli pieces and remaining cauliflower rice (can still be frozen, just break up any chunks). Pour cream sauce over everything and carefully stir to evenly incorporate and spread in an even layer. Top with remaining cup grated cheese and crushed buttery crackers, if using.
Bake for 1 hour, then allow to cool 15 minutes before enjoying. Leftovers will keep tightly sealed in the fridge up to 4 days or frozen 6-8 months. I suggest freezing in pint containers, which are about 1 serving each.