01 - Preheat oven to 400°F. Lightly grease a baking dish or line with parchment paper.
02 - In a medium mixing bowl, combine the softened cream cheese, mashed blackberries, diced jalapeño, shredded mozzarella, minced garlic, salt, and pepper. Stir until smooth and evenly incorporated.
03 - Pat the 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 - Generously fill each pocket with the blackberry-jalapeño cream cheese mixture. Secure the openings with toothpicks if needed to keep the filling enclosed.
05 - Brush both sides of each stuffed breast with olive oil. Evenly sprinkle with smoked paprika, dried thyme, and additional salt and pepper to taste.
06 - Arrange the stuffed breasts in the prepared baking dish. Bake for 28 to 32 minutes, until the chicken reaches 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 plate immediately.