01 - Preheat oven to 400°F (200°C).
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/74°C).
07 - Remove toothpicks, let rest 5 minutes, then slice and serve.