01 - Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish with olive oil or cooking spray.
02 - Pat the chicken breasts dry with paper towels. Using a sharp knife, cut a pocket lengthwise into each breast, being careful not to cut all the way through. Season the inside and outside generously with salt and pepper.
03 - In a small mixing bowl, combine the softened goat cheese, halved blackberries, finely diced jalapeño, chopped basil, and honey. Gently fold the mixture together until evenly incorporated.
04 - Spoon the blackberry-jalapeño filling evenly into the pocket of each chicken breast. Secure the openings with toothpicks to keep the stuffing inside during cooking.
05 - Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Sear the stuffed chicken breasts for about 2 minutes per side until a golden crust forms.
06 - Transfer the seared chicken breasts to the prepared baking dish. Top each breast evenly with shredded mozzarella cheese and drizzle with the remaining tablespoon of olive oil.
07 - Bake for 22 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the mozzarella is bubbly and melted.
08 - Remove from the oven and let the chicken rest for 3 to 5 minutes. Carefully remove the toothpicks and serve warm, garnished with additional fresh basil if desired.