Preheat and prep: Heat the oven to 375°F (190°C).
Grease a 9x13-inch baking dish with nonstick spray or butter.
Par-cook the broccoli: Steam fresh florets for 2–3 minutes until bright green and just tender. If using thawed frozen broccoli, pat it dry well. This prevents a watery bake.
Cook the chicken: Season chicken pieces lightly with salt and pepper.
Heat olive oil in a large skillet over medium-high. Sear chicken for 4–5 minutes, stirring occasionally, until just cooked through. Transfer to a plate.
Sauté aromatics: In the same skillet, reduce heat to medium.
Add butter and the diced onion. Cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds until fragrant.
Make the sauce: Sprinkle flour over the onion mixture and stir for 1 minute.
Slowly whisk in chicken broth until smooth, then add milk. Stir in Dijon, paprika, salt, and pepper. Simmer 2–3 minutes until slightly thickened.
Add the cheeses: Remove skillet from heat.
Stir in 1.5 cups cheddar and all the Parmesan until melted. Fold in sour cream or Greek yogurt. Taste and adjust seasoning.
Combine the bake: In a large bowl, mix the chicken, broccoli, and optional rice or pasta.
Pour the cheese sauce over and toss to coat evenly.
Assemble: Transfer mixture to the prepared baking dish. Smooth the top and sprinkle with the remaining 1/2 cup cheddar.
Bake: Bake uncovered for 18–22 minutes, until the edges bubble and the top is golden in spots.
Rest and serve: Let it rest 5 minutes to set. Serve warm with a side salad or crusty bread.