Prep the oven and pan: Heat your oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish.
Partially cook the veggies: Steam or microwave the broccoli and cauliflower just until crisp-tender, about 3–4 minutes. Drain well and pat dry to avoid a watery casserole.
Sauté aromatics: In a skillet, heat olive oil or butter over medium heat. Cook the onion 3–4 minutes until soft, then add garlic for 30 seconds until fragrant.
Remove from heat.
Make the creamy sauce: In a large bowl, whisk cream cheese, sour cream, and chicken broth until smooth. Stir in Dijon, smoked paprika, thyme, 1 cup of the shredded cheese, and a good pinch of salt and pepper.
Combine: Add cooked chicken, sautéed onions and garlic, and the drained broccoli and cauliflower to the bowl. Toss until everything is coated in the sauce.
Assemble: Spread the mixture evenly in the prepared baking dish.
Sprinkle the remaining 1/2 cup cheese over the top.
Bake: Bake for 18–22 minutes, until the casserole is bubbling and the cheese is melted and lightly golden.
Finish and serve: Let it rest 5 minutes. Garnish with chopped parsley, taste, and adjust salt and pepper if needed. Serve warm.