Combine thyme, salt, pepper, onion powder and garlic together in a medium bowl and set aside.
In a medium, oven-safe skillet, heat the butter and a tablespoon of olive oil. Add the mushrooms and stir, and cook until soft and caramelized, about 4 minutes.
Stir in the garlic and cook for about 30 seconds until it becomes fragrant.
Remove mushrooms and garlic from the pan and set them aside to cool
Cut a slit into the side of each chicken breast lengthwise to make a pocket, but don’t cut all the way through.
Season both the inside and outside of the chicken breasts with the spice mixture, rubbing it in.
Heat the oven to 400 degrees F / 200 degrees C.
Wipe the inside of the pan with a paper towel and add the remaining tablespoon of oil. Sear the chicken for 2-3 minutes on each side, or until a nice crust forms.
Turn the heat off, remove the chicken from the pan, and set it aside.
In a large bowl, mix the cream cheese until smooth, then add the mozzarella and parmesan cheese and stir to combine. Add the mushrooms and stir once more.
Gently open the chicken breasts where you sliced them and insert half of the cream cheese mixture into each pocket of the chicken breasts.
Close the breasts and seal with several toothpicks, then place the chicken breasts back into the skillet.
Bake for 15-20 minutes or until an instant thermometer reads 165 degrees F / 74 degrees C when inserted into the thickest part of the breasts.
Let the chicken rest for 5 minutes before garnishing with freshly chopped parsley or fresh thyme sprigs.