Preheat your oven to 375°F (190°C).
Using a sharp knife, make a pocket in each pork chop by slicing horizontally into the side of the chop, being careful not to cut all the way through.
Season the pork chops inside and out with the salt and pepper.
In a skillet over medium heat, heat 1 tablespoon of olive oil. Add the sliced mushrooms and sauté for 2-3 minutes. Add the minced garlic with a pinch of salt and black pepper. Continue to sauté the mushrooms until they are tender and any excess moisture has evaporated, about 3-5 minutes. Remove from heat and set aside.
Combine the basil pesto, sautéed mushrooms, and grated mozzarella cheese in a mixing bowl. Mix everything together until well combined.
Stuff each pork chop with the pesto-mushroom-cheese mixture, dividing it evenly among the chops. Press the stuffing gently into the pocket to ensure it's packed in tightly.
Secure the opening of each pork chop with toothpicks to keep the stuffing in place.
Heat 1 tablespoon of olive oil in a large oven-safe skillet over medium-high heat. Once hot, add the stuffed pork chops and sear them on each side until golden brown, about 2-3 minutes per side.
Transfer the skillet to the preheated oven and bake the stuffed pork chops for 15-20 minutes, or until they reach an internal temperature of 145°F (63°C) for medium doneness.
Once cooked through, remove the pork chops from the oven and let them rest for a few minutes before serving.
Garnish with chopped fresh parsley.