Arrange chicken breasts in the slow cooker so that they are no overlapping.
In a medium bowl, whisk together honey, soy sauce, blackberry jam, olive oil, garlic, onion and then pour over the chicken. Cover the slow cooker and cook the chicken on LOW for 4-5 hours until the chicken is fully cooked.
Using tongs, remove the chicken from the slow cooker (reserving the liquids) and place it on a cutting board. Remove the bones and use two forks to shred the chicken into smaller pieces. Place the shredded chicken in a large bowl.
In a small bowl, whisk together cornstarch with 3 T cold water to make a slurry.
Transfer liquids from the slow cooker into a small saucepan set over medium-high heat and whisk in the slurry. Bring the sauce to a boil and cook it until it reduces and has thickened slightly, about 4 minutes. Pour the sauce over the chicken , tossing to combine. Serve chicken topped with sliced scallions.
Option to our only a portion of the sauce over the shredded chicken. Any leftovers can be served with other proteins or vegetables.