Make the Mushroom Filling: In a skillet over medium heat, melt the butter. Add the sliced mushrooms and sauté for 3-4 minutes, allowing them to soften. Stir in the minced garlic and chopped parsley, cooking for another 1-2 minutes until fragrant. Season with a pinch of salt and pepper, then remove from heat and set aside.
Prepare the Chicken: Preheat the oven to 375°F (190°C). Season each chicken breast with salt, pepper, onion powder, and dried parsley. Stuff each pocket with a couple of spoonfuls of the mushroom filling and two slices of mozzarella cheese. Secure with toothpicks if necessary.
Sear the Chicken: Heat a bit of olive oil in a large, oven-safe skillet over medium-high heat. Place the stuffed chicken breasts in the pan and sear for 2-3 minutes on each side, or until they are golden and crispy. Transfer the skillet to the preheated oven and bake for 15–20 minutes until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Make the Garlic Parmesan Cream Sauce: While the chicken is baking, make the sauce. In a small saucepan, heat 1 tablespoon of olive oil over medium heat. Add the garlic and cook for 1 minute. Stir in the Dijon mustard, half-and-half, Parmesan cheese, salt, and pepper. Bring the mixture to a simmer and cook for 2-3 minutes. For a thicker sauce, incorporate the cornstarch mixture and continue cooking until it thickens to your liking. Remove from heat and fold in the chopped parsley.
Assemble and Serve: Remove the chicken from the oven and let it rest for a few minutes. Serve the chicken with a generous spoonful of garlic Parmesan cream sauce on top. Garnish with extra parsley if desired.