Prep the oven and dish: Heat the oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Blanch the broccoli: Bring a pot of salted water to a boil. Add broccoli and cook for 1–2 minutes until bright green and crisp-tender.
Drain and run under cold water to stop cooking. Pat dry.
Make the roux: In a medium saucepan over medium heat, melt 3 tablespoons butter. Whisk in flour and cook 1 minute, stirring, to remove the raw flour taste.
Build the sauce: Slowly whisk in chicken broth, then milk or half-and-half.
Simmer 2–3 minutes until slightly thickened.
Add flavor: Off the heat, whisk in mayonnaise, sour cream, 1 cup cheddar, Parmesan, curry powder, garlic powder, onion powder, lemon juice, salt, and pepper. Taste and adjust curry, salt, and lemon as needed. The sauce should be creamy and well-seasoned.
Layer the casserole: Spread broccoli evenly in the baking dish.
Scatter the chicken over the top. Pour the sauce over everything, gently spreading to cover.
Make the topping: In a small bowl, melt the remaining 1 tablespoon butter. Toss panko with melted butter and olive oil.
Stir in the remaining 1/2 cup cheddar and a pinch of salt. Sprinkle over the casserole.
Bake: Bake 20–25 minutes, until bubbling at the edges and the topping is golden. If needed, broil 1–2 minutes for extra color, watching closely.
Rest and serve: Let it sit 5–10 minutes to set.
Serve with rice, buttered noodles, or a simple green salad.