Cut the chicken breasts in half lengthwise, and pound out the thicker areas so that the halved breasts are uniform in thickness. Once pounded out, the chicken pieces should be about the same size as your hamburger buns.
Spread all purpose flour out in a wide-bottomed bowl.
Heat griddle until it reaches about 375 degrees F.
While griddle is heating, liberally sprinkle each piece of chicken with barbecue rub or seasoning. Then, lightly dredge each piece with a thin coating of all purpose flour. Shake off the excess flour.
Add about 2-3 tablespoons of your favorite cooking oil to the heated surface. Place the chicken breasts on the griddle in the oil and allow to cook on the first side untouched for about 5-7 minutes. When the chicken breasts have developed a bit of char and a nice golden brown color, flip to the second side and continue to cook until the chicken reaches an internal temp of 165 degrees F. As the chicken is cooking on the griddle, use a spatula or scraper to direct the excess oil towards the chicken breasts to shallow fry them. If needed, you can add a bit more oil to the griddle.
As each piece of chicken reaches 165 degrees F, remove it from the griddle.
While the chicken is cooking, heat your barbecue sauce in a small saucepan on the griddle. *If you are making the onion bacon jam, I recommend a tangier vinegar-based barbecue sauce to offset the sweetness of the jam. You can also add some apple cider vinegar to taste to your regular barbecue sauce in the saucepan.
Toast brioche buns cut side down on the griddle until nicely golden.
In a large bowl, add the cooked warm chicken breasts and just enough barbecue sauce to coat each piece. Toss together and serve immediately.
Add a spoonful of the onion bacon jam to the bottom of a toasted brioche bun. Top with one piece of barbecue chicken and your favorite BBQ sandwich toppings like pickles or sliced raw onion.