Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
Step 2: Season the boneless, skinless chicken breasts with salt and pepper. In a large skillet, heat a tablespoon of olive oil over medium-high heat. Briefly sear the chicken for 2-3 minutes per side until lightly browned, but not cooked through. Remove chicken from skillet and place in the prepared baking dish.
Step 3: In a medium bowl, whisk together the condensed cream of chicken soup, condensed cream of mushroom soup, milk, sour cream, dried parsley, and garlic powder until smooth. Season with a pinch more salt and pepper to taste.
Step 4: Pour the creamy soup mixture evenly over the seared chicken breasts in the baking dish.
Step 5: Sprinkle the shredded Swiss cheese generously over the top of the soup mixture.
Step 6: In another bowl, combine the Stovetop chicken stuffing mix with the melted butter. Toss gently until the stuffing is thoroughly coated.
Step 7: Evenly spread the buttered stuffing mixture over the Swiss cheese layer.
Step 8: Bake for 30-35 minutes, or until the chicken is cooked through (internal temperature reaches 165°F/74°C), the sauce is bubbly, and the stuffing topping is golden brown and crispy.
Step 9: Remove the casserole from the oven and let it rest for 5-10 minutes before serving. This allows the sauce to set and makes for easier slicing.