01 - Preheat oven to 400°F. Line a baking sheet with parchment paper or aluminum foil.
02 - In a mixing bowl, lightly mash the fresh blackberries. Add the softened cream cheese, 2 tablespoons honey, diced jalapeño, lemon zest, and a pinch of salt. Stir until well combined.
03 - Pat the chicken breasts dry with paper towels. Using a sharp knife, cut a pocket into the thickest side of each breast, being careful not to cut all the way through.
04 - Generously fill each pocket with the blackberry cream cheese mixture, distributing it evenly among the four breasts.
05 - In a small bowl, combine the olive oil, smoked paprika, garlic powder, 1/2 teaspoon salt, and ground black pepper. Brush the seasoning mixture evenly over the outside of each stuffed chicken breast.
06 - Place the stuffed chicken breasts on the prepared baking sheet. Whisk together 2 tablespoons honey and balsamic vinegar, then brush the glaze over the top of each breast.
07 - Bake for 30 to 35 minutes, or until the chicken is cooked through with an internal temperature of 165°F and the juices run clear.
08 - Remove from the oven and let the chicken rest for 5 minutes before serving. Spoon any accumulated blackberry juices from the pan over the top if desired.