Prepare the filling ingredients. Pat the sun dried tomatoes dry with paper towels and chop finely. Mince the garlic. Freshly grate the cheeses and add all the remaining filling ingredients into a medium bowl.
Mix the filling ingredients together until well combined. Divide the filling evenly into four pieces.
Carefully slice horizontally into the middle of each chicken breast to create a pocket. Cover the breast with plastic wrap, then gently pound the chicken to tenderize and create evenly thick breasts.
Season the chicken breast with garlic parsley salt and paprika on all sides. Take one divided portion of the filling mixture, and gently push it into the pocket of each chicken breast.
Heat up one tablespoons of olive oil on a skillet over medium-high heat. Add the stuffed chicken breasts and sear on each side for 3-4 minutes, or until they are golden brown in color.
Move the chicken to the oven. Bake at 350°F for about 10-20 minutes, or until the juices run clear and the internal temperature of the chicken reaches 165°F. The cooking time depends on the size and thickness of the chicken breasts.
Meanwhile in a new pan, sauté the onions for a few minutes. Add the mushrooms and continue cooking until the onions are translucent and the mushrooms are soft, about 6-8 minutes.
Sprinkle in one tablespoons of flour and stir together, cooking until no more white flour remains.
Slowly whisk in the cooking wine and scrape the bottom of the pan to deglaze. Add the broth and heavy cream. Bring it to a light boil and cook until the sauce thickens, about 8 minutes. Season the sauce to taste with salt.
Once the chicken has baked, pour the sauce over it and serve with your favorite side!