Preheat your oven to 350 degrees F. Lightly grease a 9x13-inch baking dish.

In a large pot or Dutch oven, melt 2 tablespoons of butter over medium heat. Season the chicken pieces with half the salt, half the pepper, and the Italian seasoning. Add the chicken to the pot and cook, stirring occasionally, until golden and cooked through, about 5 to 6 minutes. Use a slotted spoon to transfer the chicken to a plate and set aside.

To the same pot, add the olive oil, wild rice blend, and chicken broth. Bring to a boil over high heat, then reduce the heat to low, cover, and simmer for 20 minutes. The rice will still be slightly firm.

Stir in the broccoli florets, replace the lid, and continue simmering for another 10 minutes, or until the rice is tender and most of the liquid has been absorbed. If any liquid remains, cook uncovered for a minute or two.

Remove the pot from the heat and let it sit, covered, for 10 minutes. Do not stir; this helps any rice stuck to the bottom release easily.

Add the cooked chicken, cream of chicken soup, milk, sour cream, dried thyme, garlic powder (if using), and half of the shredded cheddar cheese. Stir gently until everything is well combined.

Transfer the mixture to the prepared baking dish and spread it evenly. Sprinkle the remaining cheddar cheese over the top. Cover the dish with foil and bake for 15 minutes.

While the casserole bakes, mix the crushed Ritz crackers with the 2 tablespoons of melted butter. After 15 minutes, remove the foil, sprinkle the cracker topping evenly over the casserole, and bake uncovered for an additional 10 minutes, until the topping is golden and the casserole is bubbly. Let it rest for 5 minutes before serving.