Make the jerk spice rub by mixing together the allspice, nutmeg, cinnamon, garlic powder, ginger, black pepper, cayenne pepper and salt together in a small bowl. Set aside.

Holding the knife horizontally, insert it into the thick end of each chicken breast and cut to make a deep pocket. Be careful not to pierce through the other end.

In a bowl, mix together the cream cheese, mozzarella cheese and ¼ cup apricot jam until well combined.

Spoon the cheese mixture evenly into the pockets of each chicken breast.

Sprinkle the jerk seasoning all over the stuffed chicken breasts and gently rub the spice into the meat.

Make the glaze, by blending the remaining ¼ cup apricot jam, scotch bonnet pepper and rum until smooth. Set aside.

Set the smoker to 250ºF using wood bisquettes of choice (maple or hickory also work great).

Place the chicken breasts on smoker rack and put the rack in the Bradley smoker. Smoke the chicken until they reach an internal temperature of 165ºF, about 3 hours.

Midway through the smoking session, brush some of the glaze on the chicken. Brush them again when the chicken comes out of the smoker.