Preheat the oven to 375 degrees Fahrenheit. If you are not using a skillet that is going from stove to oven, grease a casserole dish lightly with a small amount of butter or oil.
In a large skillet, heat the butter or oil over medium heat. Add the chopped onion and minced garlic, cooking until the onion becomes translucent and fragrant, about 3 to 4 minutes.
Increase the heat to medium-high and add the mushrooms. Sauté until they release their moisture and start to brown, about 5 to 7 minutes. This step concentrates the mushroom flavor and adds color to the dish.
Push the vegetables to the side and add the chicken pieces. Season with a pinch of salt and pepper. Cook until the chicken is just beginning to brown on the outside, about 4 to 5 minutes. It doesn’t need to be fully cooked through at this stage because it will finish in the bake.
Sprinkle the flour over the chicken and vegetables. Stir well to coat, cooking for about 1 minute to eliminate the raw flour taste.
Slowly whisk in the chicken stock and cream, bringing the mixture to a gentle simmer. The sauce will begin to thicken as it cooks. Stir in the thyme and half of the grated cheese, saving the rest for topping.
Taste and adjust the seasoning with salt and pepper. If you like a touch more brightness, add a small squeeze of lemon juice or a pinch of nutmeg for warmth.
Transfer the creamy mixture to a casserole dish. Sprinkle with the remaining cheese and breadcrumbs if you are using them. Drizzle a teaspoon of olive oil over the top to help the topping brown.
Bake in the preheated oven for 20 to 25 minutes, or until the top is golden and bubbly and the chicken is cooked through to an internal temperature of 165 degrees Fahrenheit.
If you prefer a crisper topping, switch the oven to broil for the last 2 to 3 minutes of cooking, watching closely to prevent burning.
Garnish with chopped fresh parsley and serve hot. This dish pairs wonderfully with a light salad, steamed vegetables, or a simple side of rice or mashed potatoes to soak up the creamy sauce.