Add chicken to slow cooker.
In a small bowl mix together apricot jam, mustard, Worcestershire sauce, chopped banana peppers, 2 teaspoons of vinegar, 1/4 teaspoon salt, 1/4 teaspoon pepper, and minced garlic. Pour over chicken in slow cooker. Cook on low for 4-5 hours.
Slice cabbage and grate carrot. Toss into a mixing bowl. Thinly slice radishes and basil leaves. Add to mixing bowl along with sunflower seeds, lime juice, olive oil, 1 teaspoon vinegar, 1/4 teaspoon salt and 1/4 teaspoon pepper. Toss well and allow to rest at room temp for 15 minutes.
Once chicken is done, shred it. Whisk together the cornstarch and water. Add to chicken and mix thoroughly. Cover and allow to cook at high for 5 minutes.
Add chicken to each bun along with cabbage mixture on top. Serve with grapes.