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 of each breast 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 well combined.
04 - Spoon the blackberry-jalapeño mixture evenly into the pocket of each chicken breast. Secure the openings with toothpicks if needed to keep the filling 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 golden brown.
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 is cooked through and the cheese is bubbly and melted. The internal temperature of the chicken should reach 165°F.
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 if desired and serve warm.