Heat a drizzle of EVOO in a saucepot over medium-high heat. Add the bacon and brown to crisp. Then add the garlic and onions and stir to soften, about 3 minutes. Add the ketchup, stock, syrup, mustard, Worcestershire, vinegar and pepper. Stir and simmer to thicken, 20 minutes.
Heat a drizzle of EVOO in a large skillet over medium-high heat, add the butter and melt. Add the apples and red onions. Season with some salt, pepper and nutmeg. Cook to tender-crisp, 5 to 6 minutes. Add the chicken and sauce and combine. Cool and store for a make-ahead meal. Reheat over medium heat and serve the BBQ chicken, apples and onions on the rolls topped with cheese and pickles.