Add all your Jerk seasoning ingredients (except the chicken) to the bowl of a food processor or blender and pulse until you have a rough paste.
Add your chicken thighs or breast meat to a large zip-top bag.
Once you have a paste-like jerk seasoning, pour it into the bag with your chicken, remove as much air as possible from the bag and seal. Massage the chicken and the seasoning in the bag until most of the chicken seems like it's covered by the jerk seasoning paste.
Place the bag with jerk seasoned chicken into the refrigerator and let it rest overnight or at least 8 hours.
Once your chicken has been resting in the jerk seasoning for at least 8 hours, you can remove it from the bag and prepare it for grilling. I suggest doing this outdoors if you can over medium-high heat of a charcoal or gas grill. Cook each piece of chicken for around 5 minutes per side or until it reaches an internal temperature of 165 degrees F (74 C). You can grill this indoors on a grill pan as well or cook in a skillet if you'd prefer that.
WARNING: If you cook this indoors, make sure you have an exhaust fan running or open a window because this marinade may cause you to cough if you inhale a lot of it during the cooking process.
If you plan to have cheese on your sandwiches, I suggest you add the cheese when there are about 2 minutes of cooking time left on the grilling process. Place the cheese on top of the fully cooked side and the cheese will get all soft and melty while the other side of the chicken finishes cooking.
Once the chicken is fully cooked, move them all to a plate to rest. At this point, I like to toast my buns. You can toast them on the grill or pan that you just used or if the pan is too messy from the chicken cooking, you can toast under a broiler. The goal is just to get a bit of crunch and texture to the bun. You can skip this if you don't want toasted buns.
Add any condiments to the bottom bun and add one piece of cheese to each bottom bun.
Top each piece of chicken with slaw and the top of the toasted bun. Serve and enjoy.