01 - Preheat oven to 400°F.
02 - In a skillet over medium heat, melt butter. Add shallot and garlic; sauté for 1 minute until fragrant. Add mushrooms, thyme, oregano, salt, and pepper. Cook, stirring, until mushrooms are golden and moisture has evaporated, about 7 minutes. Remove from heat and let cool slightly. Stir in Parmesan, mozzarella, and parsley.
03 - Pat chicken dry. With a sharp knife, cut a deep pocket horizontally into the thickest side of each breast, being careful not to cut all the way through. Season inside and outside with salt and pepper.
04 - Stuff each chicken breast with the mushroom mixture, securing with toothpicks if needed.
05 - In a large oven-safe skillet, heat olive oil over medium-high heat. Sear the stuffed breasts for 2-3 minutes per side until golden.
06 - Add chicken broth to the skillet. Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and juices run clear (internal temperature 165°F).
07 - Remove toothpicks, let rest 5 minutes, then slice and serve.