Preheat the oven to 375°F (190°C).
Season the chicken breasts evenly with salt, black pepper, garlic powder, and dried thyme on both sides.
Heat olive oil in a large skillet over medium heat. Add the chicken breasts and cook for 4-5 minutes per side until golden brown but not fully cooked through. Remove chicken and set aside.
In the same skillet, add the chopped onion and celery. Sauté for 5 minutes until softened.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Sprinkle the flour over the vegetables in the skillet and stir well to combine. Cook for 1-2 minutes to remove the raw flour taste.
Gradually whisk in the chicken broth and milk, stirring constantly until the sauce thickens, about 3-4 minutes.
Remove the skillet from heat and stir in the shredded cheddar cheese until melted and smooth.
In a 9×13 inch baking dish, spread half of the prepared stuffing mix evenly on the bottom.
Place the browned chicken breasts on top of the stuffing layer.
Pour the creamy sauce evenly over the chicken breasts.
Spread the remaining stuffing mix over the sauce layer, covering the chicken completely.
Drizzle the melted butter evenly over the top stuffing layer.
Cover the baking dish tightly with aluminum foil and bake for 30 minutes.
Remove the foil and bake uncovered for an additional 15 minutes until the top is golden brown and the chicken is cooked through (internal temperature should reach 165°F or 74°C).
Remove from oven and let rest for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.