In a medium skillet, combine chicken stock and apple juice, then bring to a gentle simmer. Add the chicken breasts and poach for about 10 minutes, turning once halfway through.
While the chicken cooks, heat olive oil in another skillet over medium-low heat. Add chopped onion and garlic, sautéing gently until soft and fragrant.
In a bowl, mix tomato paste, brown sugar, Worcestershire sauce, hot sauce, grill seasoning, and chopped sweet pickles.
Once the chicken is cooked through, transfer a couple of ladles of the poaching liquid into the sauce mixture and stir well.
Remove the chicken, slice it, then shred it using two forks. Add the shredded chicken to the sauce mixture and toss to coat.
Transfer the sauced chicken into the skillet with onions and garlic. Simmer for 5–10 minutes until thick and flavorful.
Mix the sour pickle with the sweet pickles to create a quick relish.
Fill each bun with the shredded BBQ Chicken Sammies mixture and top with pickle relish. Serve warm.