Preheat the oven to 375°F. Grease a 9 x 13-inch baking dish.
Steam broccoli for 3–4 minutes (or blanch for 2 minutes), then drain well and set aside.
Make the sauce: melt butter in a saucepan over medium heat. Add onion and cook 3–4 minutes. Add garlic and cook 30 seconds.
Stir in flour and cook 1–2 minutes.
Whisk in chicken broth, then milk. Simmer 3–5 minutes, stirring often, until thickened.
Remove from heat and stir in sour cream, Dijon, lemon juice, salt, pepper, and nutmeg. Taste and adjust seasoning.
Add chicken and broccoli to the baking dish. Pour sauce over the top and stir gently to combine.
Sprinkle cheddar and parmesan evenly over the top.
Optional: mix panko with melted butter or olive oil, then sprinkle over the cheese.
Bake 20–25 minutes, until bubbling and golden. Rest 10 minutes before serving.