Preheat your oven to 375°F (190°C). Make a deep pocket in each chicken breast and season with salt and pepper.
Melt butter in a skillet over medium heat. Sauté chopped mushrooms until golden brown, add minced garlic and thyme, then remove from heat and let cool.
Combine the sautéed mushrooms with cream cheese and half of the mozzarella in a mixing bowl.
Fill each chicken breast with the mushroom filling, securing edges if necessary.
Heat olive oil in a large oven-safe skillet over medium-high heat. Sear each chicken breast for 3-4 minutes on each side until golden brown. Sprinkle with remaining mozzarella.
Transfer the skillet to the oven and bake for 20-25 minutes until cooked through and cheese is bubbly.
Let the chicken rest for 5 minutes, garnish with parsley, and serve.
