Prep the Chicken Pockets: Pat the chicken breasts dry with a clean paper towel. Place a breast flat on a cutting board. Using a sharp knife, slice a clean horizontal pocket into the thickest part of the side, taking care not to cut all the way through to the other side. Season the inside and outside of the chicken breasts evenly with salt, black pepper, and dried oregano.

Cook the Garlic Butter Mushrooms: Melt the unsalted butter in a large skillet over medium-high heat. Add the thin-sliced mushrooms. Cook, stirring occasionally, for 5 to 7 minutes until they turn a deep golden brown. Stir in the minced garlic and cook for 1 minute until highly fragrant. Remove the skillet from heat and allow the mixture to cool slightly.

Stuff the Chicken: In a small clean bowl, mix together the shredded mozzarella and grated parmesan cheese. Open each chicken pocket up and stuff it with a generous spoonful of the cooked garlic butter mushrooms, followed by a handful of the mixed cheeses. Reserve a small handful of cheese and a few mushroom slices for the top topping later. Press the open edges of the pocket firmly together. (Secure with wooden toothpicks if needed).

Sear and Bake: Preheat your oven to 400°F (200°C). Heat 1 tablespoon of extra virgin olive oil in an oven-safe skillet or pan over medium-high heat. Sear the stuffed chicken breasts for 3-4 minutes on each side until deep golden brown. Transfer the chicken breasts to a greased baking dish. Top each breast with the reserved cheese and mushroom slices. Bake in the preheated oven for 20 to 25 minutes, or until the internal temperature reaches exactly 165°F (74°C).

Garnish and Serve: Remove the dish from the oven and let the chicken rest for 5 minutes to keep it juicy. Garnish with plenty of freshly chopped flat-leaf parsley and spoon the remaining garlic butter pan juices over the top before serving.