Preheat the oven to 400°F (200°C).
Melt the butter in a large oven-safe skillet over medium heat. Add 4 minced garlic cloves and cook for about 30–60 seconds, just until fragrant.
Add the sliced mushrooms. Season lightly with salt and black pepper, then add 2 tablespoons chopped parsley.
Cook the mushrooms, stirring occasionally, until tender and lightly browned. Transfer them to a bowl to cool, leaving the flavorful garlic butter and mushroom juices in the skillet.
Pat the chicken breasts dry with paper towels. Season both sides with salt, black pepper, onion powder, and dried parsley.
Carefully cut a horizontal pocket through the thickest side of each chicken breast without slicing completely through to the other side.
Place 2 mozzarella slices inside each pocket.
Divide the cooked mushroom mixture among the four chicken breasts, reserving any excess mushrooms for the sauce. Spoon approximately 1 tablespoon grated Parmesan into each chicken pocket.
Secure each opening with 2–3 toothpicks to help keep the filling inside during cooking.
Return the skillet containing the garlic butter juices to medium-high heat. Add the olive oil if the pan seems dry.
Place the stuffed chicken breasts in the hot skillet. Sear until golden on the first side, then carefully turn and brown the other side.
Cover the oven-safe skillet and transfer it to the preheated oven.
Bake the Mushroom Stuffed Chicken for approximately 18–22 minutes, or until the thickest part of the chicken reaches a safe internal temperature of 165°F (74°C).
Transfer the cooked chicken to a warm plate and carefully remove the toothpicks. Keep the pan juices in the skillet if making the cream sauce.
Place the skillet over medium-low heat. Add 2 minced garlic cloves to the remaining pan juices and cook for about 30–60 seconds.
Reduce the heat and stir in the Dijon mustard and half-and-half.
Bring the sauce to a gentle simmer. Add any remaining mushrooms and the 1/2 cup grated Parmesan.
Stir gently until the cheese melts and the sauce becomes smooth.
If you prefer a thicker sauce, stir together the cornstarch and water. Gradually whisk the slurry into the simmering sauce until it reaches your desired consistency.
Season with salt and black pepper, then stir in the fresh parsley.
Return the chicken to the skillet and spoon the warm garlic Parmesan cream sauce over the top before serving.