Place the chicken in a saucepan or Dutch oven with the chicken stock or water. Bring to a boil, cover the pot, reduce heat to a simmer and cook until the chicken is cooked through, about 20 – 25 minutes. Remove the chicken from the liquid, let cool enough to handle then remove the skin and bones and shred.

Puree the maraschino cherries along with their liquid in a blender. Pour into a large saucepan and add the ketchup, pineapple juice, Worcestershire sauce, garlic, onion, and chipotle chili powder. Stir to combine. Bring to a boil, reduce heat and simmer, uncovered, until thickened to the consistency of barbecue sauce, about 30 minutes. Add the shredded chicken to the sauce, stirring to combine.

In a large mixing bowl, combine the sour cream, mayonnaise, sugar, and lime juice, whisking until smooth. Add the cole slaw, green onions, and cilantro. Toss to combine. Season to taste with salt and pepper.

Place some chicken on the bottom half of a hamburger bun, top with cole slaw and the top half of the bun.