01 - Preheat oven to 400°F. Lightly grease a baking dish or line with parchment paper.
02 - In a medium bowl, combine cream cheese, mashed blackberries, diced jalapeño, mozzarella, garlic, salt, and pepper. Mix until smooth and well incorporated.
03 - Pat chicken breasts dry with paper towels. Using a sharp knife, carefully cut a horizontal pocket into the thickest part of each breast, stopping before slicing all the way through.
04 - Fill each chicken breast pocket with the blackberry-jalapeño cheese mixture, distributing evenly. Secure the openings with toothpicks if needed to hold the filling inside.
05 - Brush both sides of each stuffed chicken breast with olive oil. Season evenly with smoked paprika, dried thyme, salt, and pepper.
06 - Arrange the stuffed chicken breasts in the prepared baking dish. Bake for 28 to 32 minutes, until the internal temperature reaches 165°F and the filling is bubbly and melted.
07 - Remove from the oven and let rest for 3 to 5 minutes. Remove toothpicks before serving.