Prepare the Filling:
Heat olive oil in a skillet over medium heat. Add mushrooms and sauté until browned and tender, about 5–6 minutes. Add garlic and thyme, cook another minute. Let cool slightly, then mix with mozzarella and Parmesan.
Stuff the Chicken:
Cut a pocket into each chicken breast by slicing horizontally without cutting all the way through. Season the outside of each breast with salt, pepper, and Italian seasoning. Stuff each pocket with the mushroom-cheese mixture and secure with toothpicks.
Sear the Chicken:
Heat 1 tbsp olive oil and 1 tbsp butter in a skillet over medium-high heat. Sear the stuffed chicken for 3–4 minutes per side until golden brown.
Bake Until Cooked Through:
Transfer skillet to a 375°F (190°C) oven (or place chicken in a baking dish). Bake for 15–20 minutes, or until chicken reaches an internal temperature of 165°F (74°C).
Make the Garlic Butter Sauce:
While chicken bakes, melt 2 tbsp butter in a small pan over low heat. Add minced garlic and parsley, and cook for 1–2 minutes until fragrant.
Serve:
Drizzle garlic butter over the stuffed chicken and serve hot. Delicious with mashed potatoes, roasted vegetables, or a simple salad.