01 - Preheat oven to 375°F. Lightly grease a baking dish with olive oil or cooking spray.
02 - Pat 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 inside and out with salt and pepper.
03 - In a small mixing bowl, combine softened goat cheese, halved blackberries, finely diced jalapeño, chopped basil, and honey. Gently fold together until evenly incorporated.
04 - Spoon the blackberry-jalapeño mixture generously into each chicken breast pocket. Secure the openings with toothpicks to keep filling enclosed during cooking.
05 - Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Sear stuffed chicken breasts for about 2 minutes per side until a golden crust forms.
06 - Transfer seared chicken breasts to the prepared baking dish. Top each breast evenly with shredded mozzarella and drizzle with remaining 1 tablespoon olive oil.
07 - Bake for 22-25 minutes until chicken is cooked through (internal temperature reaches 165°F) and cheese is bubbly and melted.
08 - Remove from oven and let rest for 3-5 minutes. Carefully remove toothpicks and serve warm, garnished with additional fresh basil if desired.