1. Prepare Ingredients (10 minutes):
* Cut the chicken into 1-inch pieces and season lightly with salt and pepper.
* Chop the broccoli into bite-sized florets. If the stems are thick, you can peel and dice them too.
* Finely chop the onion (if using) and mince the garlic.
* Shred the cheddar cheese and grate the Parmesan.
* If using a breadcrumb topping, mix the panko/Ritz crackers with 1 tablespoon of melted butter in a small bowl. Set aside.

2. Cook the Chicken (5-7 minutes):
* Heat 1 tablespoon of olive oil or butter in a large, oven-safe skillet (at least 10-12 inches, cast iron is great) over medium-high heat.
* Add the seasoned chicken pieces in a single layer (cook in batches if necessary to avoid overcrowding).
* Sear the chicken for 2-3 minutes per side, until lightly browned but not necessarily cooked all the way through. It will finish cooking in the sauce.
* Remove the chicken from the skillet and set aside on a plate.

3. Sauté Aromatics and Broccoli (5-7 minutes):
* To the same skillet, add the remaining 1 tablespoon of olive oil or butter if needed.
* Add the chopped onion (if using) and cook over medium heat for 2-3 minutes, until softened.
* Add the minced garlic and cook for another minute until fragrant.
* Add the broccoli florets to the skillet. Sauté for 3-5 minutes, stirring occasionally, until they turn bright green and are slightly tender-crisp. You can add a tablespoon or two of water or chicken broth and cover the skillet for a couple of minutes to help steam the broccoli if you prefer it softer.
* Remove the broccoli from the skillet and set aside (you can add it to the plate with the chicken).

4. Make the Creamy Cheese Sauce (8-10 minutes):
* In the same skillet, melt 3 tablespoons of butter over medium heat.
* Once melted, whisk in 3 tablespoons of all-purpose flour. Cook, whisking constantly, for 1-2 minutes to create a roux. This cooks out the raw flour taste.
* Gradually whisk in the chicken broth, a little at a time, ensuring each addition is smooth before adding more. This prevents lumps.
* Once all the broth is incorporated, whisk in the milk or half-and-half.
* Bring the sauce to a gentle simmer, whisking frequently, until it begins to thicken (about 3-5 minutes).
* Reduce the heat to low. Stir in the shredded cheddar cheese (reserving some for topping if not using breadcrumbs) and grated Parmesan cheese. Stir until the cheese is completely melted and the sauce is smooth.
* Stir in the Dijon mustard (if using) and a pinch of nutmeg (if using).
* Taste the sauce and adjust seasoning with salt and pepper as needed. Remember the chicken and broth already have some salt.

5. Combine and Finish (5-7 minutes + Optional Broiling):
* Return the cooked chicken and sautéed broccoli to the skillet with the cheese sauce.
* Stir gently to ensure everything is well coated. Allow to simmer for a few minutes for the flavors to meld and the chicken to cook through completely.
* If using, sprinkle the buttered breadcrumb mixture (or extra reserved shredded cheese) evenly over the top.
* Optional Broiling for a Golden Top: If your skillet is oven-safe, you can place it under a preheated broiler for 2-3 minutes, watching very carefully, until the topping is golden brown and bubbly. Do not walk away, as broilers work very quickly!
* If not broiling, simply cover the skillet for a couple of minutes to melt the cheese on top.

6. Rest and Serve:
* Remove the skillet from the heat (or broiler). Let the Skillet Chicken Divan rest for a few minutes before serving. This allows the sauce to thicken slightly more.
* Garnish with fresh parsley, if desired, and serve hot.