Preheat the oven to 400°F. Place the sweet potatoes on a baking sheet and prick each one several times with a fork. Bake for 45 to 50 minutes until soft when pierced with a knife.
While the potatoes bake, place the chicken breasts in a skillet with a splash of water. Cover and simmer over medium heat for 12 to 15 minutes until cooked through. Remove the chicken, shred it with two forks, and return it to the skillet.
Pour the barbecue sauce over the shredded chicken. Stir and cook over low heat for 3 to 4 minutes until the chicken is evenly coated and warmed through. Set aside.
In a mixing bowl, combine the shredded cabbage and carrot. In a small bowl, whisk together the apple cider vinegar, honey, Greek yogurt, salt, and pepper. Pour the dressing over the vegetables and toss until well coated.
Slice each sweet potato open lengthwise and fluff the flesh slightly with a fork. Divide the BBQ chicken among the potatoes, then top each one with a generous scoop of the quick slaw. Finish with sliced green onions.