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, minced 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, taking care not to slice all the way through.
04 - Gently fill each chicken breast pocket with the blackberry-jalapeño cheese mixture. Secure the openings with toothpicks if needed to keep the filling enclosed.
05 - Brush both sides of the stuffed chicken breasts with olive oil. Evenly sprinkle 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 chicken is cooked through with an internal temperature of 165°F and the filling is bubbly and melted.
07 - Remove from the oven and let rest for 3 to 5 minutes before serving. Remove any toothpicks and serve warm.