Begin by patting the chicken dry with paper towels, then season it generously with salt and pepper. Heat a large Dutch oven over medium-high heat and add a splash of oil. Once the oil is shimmering, sear the chicken pieces until they are opaque but not fully cooked, about 3-4 minutes on each side. Remove the chicken and set it aside.

In the same Dutch oven, add the diced onion, carrots, and celery. Sauté these aromatic vegetables for about 5-7 minutes, stirring occasionally until they're tender and fragrant. Afterward, add minced garlic and sauté for another minute until you can smell the garlic's richness.

Now, in the leftover oil and juices, add sliced mushrooms to the pot. Sauté them over medium heat for about 5-6 minutes until they become deeply golden and tender. Combine the mushrooms with the sautéed vegetables and return the seared chicken to the pot.

In a separate saucepan, melt 4 tablespoons of butter over medium heat and whisk in an equal amount of flour to form a roux. Cook this mixture for about 2 minutes until it turns light golden. Gradually whisk in chicken broth and milk, stirring continuously until the sauce thickens and bubbles, around 5-7 minutes.

Once the cream sauce is thickened, pour it over the chicken and vegetable mixture. Add the pre-cooked wild rice to the pot, stirring everything gently until well combined.

Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish, then transfer the chicken and rice mixture into it. Spread the contents evenly. Top the dish with freshly grated cheddar and Parmesan cheese, followed by a sprinkle of panko breadcrumbs.

Cover the baking dish with aluminum foil and place it in the preheated oven. Bake for 30-35 minutes or until the casserole bubbles and the cheese is melted. For a golden finish, uncover it in the last 10 minutes of baking. Allow it to rest for a few minutes before serving.