Prep and preheat: Heat your oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish. Pat the chicken dry and season with salt and pepper.
Brown the chicken: In a large skillet, warm the olive oil or butter over medium-high heat. Add the chicken in a single layer.
Cook 4–5 minutes, stirring once, until lightly browned but not fully cooked. Transfer to a plate.
Sauté the aromatics: In the same skillet, add the onion with a pinch of salt. Cook 3–4 minutes until translucent.
Stir in the garlic and cook 30 seconds, until fragrant.
Cook the mushrooms: Add mushrooms and thyme. Cook 6–8 minutes, stirring occasionally, until the mushrooms release their liquid and it mostly evaporates. Sprinkle in parsley and red pepper flakes, if using.
Build the sauce: Sprinkle the flour over the vegetables.
Stir to coat and cook 1 minute. Pour in the chicken broth slowly, stirring to smooth out lumps. Simmer 2 minutes until slightly thickened.
Make it creamy: Lower the heat.
Stir in the heavy cream, sour cream, and Dijon. Taste and adjust salt and pepper. The sauce should be velvety and well-seasoned.
Combine: Return the chicken and any juices to the skillet.
Stir in peas or green beans if you’re using them. Fold in the Parmesan and half the mozzarella or Gruyère.
Assemble the casserole: Pour everything into the prepared baking dish. Top with the remaining mozzarella or Gruyère.
Optional crunchy topping: Mix panko with melted butter and a pinch of salt.
Sprinkle evenly over the top for a golden crust.
Bake: Place the dish on the center rack and bake 18–22 minutes, until bubbling around the edges and the chicken is cooked through. If you want extra browning, broil 1–2 minutes at the end, watching closely.
Rest and serve: Let it sit 5–10 minutes so the sauce settles. Garnish with chopped parsley.
Serve with rice, mashed potatoes, or a simple green salad.