Preheat the oven to 400°F.
In a 10-inch skillet, melt the butter over medium heat. Add the onion and garlic and cook until slightly softened, about 3 minutes.
Add the mushrooms and cook until juices are released and reabsorbed. Add wine and thyme. Cook until evaporated but not dry. Cool completely.
In a small bowl, combine cooled mushrooms with cream cheese, mozzarella cheese, and salt & pepper to taste.
Using a paring knife, cut a 1 ½″ slit in the side of the chicken. Move the knife around to create a pocket. Fill the pocket in each chicken breast with ¼ of the mushroom mixture.
In a small bowl, combine paprika, garlic powder, ½ teaspoon salt and ¼ teaspoon black pepper. Season the outside of the chicken.
In an ovenproof skillet, heat 1 tablespoon of oil over medium heat. Brown the chicken for about 3 minutes on each side or until golden.
Place the skillet in the oven and bake for an additional 17-21 minutes or until the chicken reaches 165°F in the thickest part.
Remove from the oven and transfer the chicken to a plate. Let rest for 5 minutes before serving.
