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 deep 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 evenly combined, keeping some berry chunks intact for texture.
04 - Spoon the goat cheese and blackberry filling generously into each chicken breast pocket. Press gently to distribute the filling evenly. 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. Once the oil shimmers, carefully place the stuffed chicken breasts in the pan. Sear each side for about 2 minutes until a golden crust forms.
06 - Transfer the seared chicken breasts to the prepared baking dish. Sprinkle the shredded mozzarella evenly over the top of each breast. Drizzle with the remaining 1 tablespoon of olive oil.
07 - Bake in the preheated oven for 22 to 25 minutes, or until the internal temperature of the chicken reaches 165°F and the mozzarella is bubbly and fully melted.
08 - Remove from the oven and let the chicken rest for 3 to 5 minutes. Carefully remove the toothpicks before serving. Garnish with additional fresh basil leaves if desired and serve warm.