01 - Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish with olive oil or nonstick spray.
02 - Pat the chicken breasts dry with paper towels. Using a sharp knife, cut a deep 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, diced jalapeño, chopped basil, and honey. Fold gently until evenly incorporated.
04 - Spoon the blackberry-jalapeño mixture into each chicken breast pocket, dividing evenly. Press gently to close and secure openings with toothpicks if needed.
05 - Heat 1 tablespoon 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 with shredded mozzarella and drizzle with the remaining 1 tablespoon olive oil.
07 - Bake for 22 to 25 minutes, or until the internal temperature of the chicken reaches 165°F and the cheese is bubbly and melted.
08 - Remove from the oven and let rest for 3 to 5 minutes. Carefully remove toothpicks before serving. Garnish with additional fresh basil if desired.