For the barbecue sauce: In a medium saucepot over medium heat, add the ketchup, apple cider vinegar, dark brown sugar, Worcestershire sauce, black pepper, garlic powder, dry mustard, onion powder, hot sauce and 1 cup water and stir to combine. Bring the mixture to a simmer, then reduce the heat to low and cook until the sauce is thickened, about 1 1/2 hours.
For the chicken: Heat a grill pan over medium-high heat.
Lightly drizzle some olive oil onto the chicken to prevent the chicken from sticking to the grill pan. Season the chicken with salt and pepper. When the grill pan is hot, add the chicken and cook until char marks appear and the chicken is cooked through, 2 to 3 minutes per side.
Toss the chicken with the barbecue sauce. Let simmer on low until ready to serve, to infuse the chicken with the flavor of the sauce.
For the sandwich: Spread an even layer of mayonnaise on the top and bottom of a potato bun, add the chicken, a few red onion slices and 2 bread and butter pickles. Top with the other half of the potato bun.