Preheat oven to 400°F. Pat the chicken breasts dry with paper towels and season with salt and pepper.
Heat 2 tablespoons butter in a large ovenproof skillet (or Dutch oven) over medium-high heat. Add the chicken and cook until well browned on one side, about 6-8 minutes. Transfer the partially cooked chicken to a plate and cover, browned side up; set aside.
Add 2 tablespoons butter to the now empty skillet along with the onions and celery. Season with ¼ teaspoon salt and ½ teaspoon pepper. Sauté until the vegetables are crisp tender. Add the garlic and sauté until fragrant, about 1 minute. Remove the vegetables to a bowl and set aside.
Melt 2 tablespoons butter in the skillet and add the mushrooms. Cook, undisturbed, until the mushrooms are well browned on one side. Stir and turn the mushrooms and continue cooking until the moisture is released and evaporated, and the mushrooms are well browned.
Add the vegetables back to the skillet with the mushrooms along with the dry wild rice blend. Cook for about 2 minutes, stirring constantly, then add the chicken broth and white wine to the skillet. Bring to a boil then reduce the heat to medium. Cover the pan and simmer until most of the liquid is absorbed, about 15 to 20 minutes, stirring occasionally. (NOTE - you may want add 10 minutes if using a different kind of rice blend that requires longer cooking - check the cooking directions for your variety. The rice should still be a little soupy and starting to soften)
While the rice is cooking, make the white sauce. In a small saucepan melt the remaining 3 tablespoons butter. Add the flour, ¼ teaspoon salt, ½ teaspoon pepper, onion powder and thyme. Cook, stirring constantly for 1 to 2 minutes. Add the milk, slowly, whisking to combine. Cook until the sauce is thickened.
Once done, remove the rice from the heat. Pour the white sauce over the top of the rice and stir lightly to combine. Place the chicken in the skillet on top of the rice and push down lightly leaving the tops uncovered. Transfer to the oven and bake, uncovered, until chicken registers 160°F (for breasts) on an instant read thermometer, about 20 to 25 minutes. Allow the casserole to cool for 10 minutes before serving.
Garnish with chopped parsley and serve.