Preheat oven to 425°F. Place the chicken breast on a cutting board and, holding your knife parallel to the board, slice horizontally through the chicken, stopping about ½-inch from the opposite edge. Open the chicken like a book to create a pocket.
Cover the butterflied chicken with plastic wrap and gently pound the thicker portions to create an even thickness of approximately ½-inch throughout.
Sprinkle the inside of each chicken breast with ¼ teaspoon salt, ¼ teaspoon pepper, and ¼ teaspoon garlic powder.
Spread 2 tablespoons of pesto evenly across the inside surface of each chicken breast, leaving a ½-inch border. Layer the mozzarella slices over the pesto, again maintaining the border.
Fold the chicken back to its original shape. Secure with kitchen twine at 1-inch intervals or use toothpicks placed at a diagonal to hold the pocket closed.
Brush the outside of each chicken breast with olive oil, then season with the remaining salt, pepper, garlic powder, and the oregano. If using, sprinkle with Parmesan cheese.
Heat an oven-safe skillet over medium-high heat. Add the chicken breasts and sear for 3-4 minutes on one side until golden brown.
Flip the chicken, then immediately transfer the skillet to the preheated oven. Reduce oven temperature to 375°F.
Cook for 15-18 minutes, or until the internal temperature reaches 160-165°F at the thickest part (avoiding the cheese pocket when measuring).
Remove from oven and let rest for 5 minutes under loose foil to allow for carryover cooking and juice redistribution.
Remove kitchen twine or toothpicks. Slice on a diagonal to showcase the filling and garnish with fresh basil leaves.