01 - Preheat the oven to 375°F. Lightly grease a 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 freshly ground black 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 well incorporated, keeping some berry texture intact.
04 - Spoon the blackberry-jalapeño filling evenly into each chicken breast pocket. Press gently to distribute the filling and secure the openings with toothpicks if needed 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. Work in batches if necessary to avoid crowding the pan.
06 - Transfer the seared chicken breasts to the prepared baking dish. Top each breast evenly with shredded mozzarella cheese and drizzle with the remaining 1 tablespoon of olive oil.
07 - Bake in the preheated oven for 22 to 25 minutes, or until the chicken registers an internal temperature of 165°F and the mozzarella is bubbly and melted on top.
08 - Remove from the oven and let the chicken rest for 3 to 5 minutes. Carefully remove any toothpicks before serving. Garnish with additional fresh basil leaves if desired and serve warm.