Melt the butter in a skillet over medium heat, then add the mushrooms. Let them cook until they’re golden brown and soft, about 5 minutes. Stir in garlic and thyme just at the end so the flavors stay fresh and fragrant. Remove from heat and set aside.
In the same skillet, toss in the spinach. It only takes about 30 seconds to wilt down nicely. Mix the spinach with the cooked mushrooms and let the filling cool slightly so it’s easier to handle.
Take each chicken breast and carefully cut a pocket inside with a sharp knife. Make sure not to slice all the way through. Sprinkle salt and pepper inside and out to season the chicken before stuffing.
Spoon the mushroom-spinach mixture into the pockets, then slide in the mozzarella slices. Tuck everything inside and secure the opening with toothpicks to keep the filling from escaping.
Heat olive oil in the skillet and sear each stuffed chicken breast for about 1–2 minutes on each side until beautifully golden. This step keeps the chicken juicy and adds flavor.
Transfer the chicken to an oven preheated to 390°F (200°C). Bake for around 15 minutes, or until the chicken reaches 165°F internally. Let it rest for 5 minutes before serving so the juices stay locked in.