Preheat the oven to 375°F (190°C).
Season the chicken breasts evenly with salt and black pepper.
Heat olive oil in a large skillet over medium heat. Add the chicken breasts and cook for 4-5 minutes on each side until golden brown but not fully cooked through. Remove chicken from skillet and set aside.
In the same skillet, add the chopped onion, minced garlic, and sliced mushrooms. Sauté for 5 minutes until the onions are translucent and mushrooms are softened.
Sprinkle the flour over the vegetables in the skillet and stir well to coat. Cook for 1 minute to remove the raw flour taste.
Gradually whisk in the chicken broth and milk, stirring constantly until the sauce thickens, about 3-4 minutes.
Add dried thyme, dried sage, and paprika to the sauce. Stir to combine and remove from heat.
In a greased 9×13 inch baking dish, spread half of the prepared stuffing evenly on the bottom.
Place the browned chicken breasts on top of the stuffing layer.
Pour the creamy mushroom sauce evenly over the chicken breasts.
Top with the remaining stuffing, spreading it evenly over the sauce.
Sprinkle shredded cheddar cheese evenly over the top layer of stuffing.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes or until the cheese is melted and bubbly and the chicken is cooked through (internal temperature reaches 165°F or 74°C).
Remove from oven and let the casserole rest for 5 minutes before serving.