Heat oven to 375°F. Grease a 9x13-inch baking dish.
Warm olive oil in a large skillet over medium heat.
Sauté cauliflower rice 5–6 minutes, stirring, until moisture cooks off. Set aside.
Steam broccoli 2–3 minutes until crisp-tender, then drain well.
Whisk cream cheese, sour cream, and heavy cream in a bowl until smooth.
Stir in garlic, onion powder, paprika, thyme, salt, and pepper.
Fold in 1 cup cheddar and all the Parmesan to make the sauce.
Combine chicken, broccoli, cauliflower rice, and sauce in a large bowl. Toss to coat.
Spread mixture in the baking dish. Top with remaining cheddar and bacon.
Bake 20–25 minutes until hot and lightly browned around edges.
Rest 5 minutes. Sprinkle green onions and serve warm.