Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
Melt butter in a small skillet over medium heat and sauté finely chopped mushrooms until moisture has evaporated and they are golden brown, approximately 5 minutes.
Transfer mushrooms to a small bowl and mix with mozzarella and parmesan cheese.
Using a sharp knife, cut a pocket into the side of each chicken breast, being careful not to cut all the way through.
Stuff the mushroom and cheese mixture evenly into the chicken pockets and secure the opening with toothpicks.
Season both sides of the chicken with salt, pepper, garlic powder, and dried oregano.
Heat olive oil in an oven-safe skillet over medium-high heat and sear the chicken for 3 minutes per side until golden.
Transfer the skillet to the oven and bake for 12 to 15 minutes, or until the internal temperature reaches 165 degrees Fahrenheit (74 degrees Celsius).
Allow the chicken to rest for 5 minutes before removing toothpicks and serving.