Using a flat meat tenderizer, pound the chicken out to an even thickness (about 3/4 of an inch). If your chicken breasts are really large, cut them in half so that they fit on the buns.
In a mixing bowl, whisk together the oil, salt, seasonings, buffalo sauce, and honey. Add the chicken and toss well to coat. Cover and refrigerate for at least 1 hour, up to 48 hours.
Preheat a grill or grill pan to medium-high heat. If you're using an outdoor grill, make sure to clean and oil the grill grates really well. If you're using an indoor grill pan, drizzle with 1 tablespoon of high-heat oil. Grill the chicken for 5 minutes on the first side, flip, and brush liberally with buffalo sauce while the other side cooks for another 5 minutes. Flip again and brush the other side with sauce. Add the cheese and allow it to melt over the chicken.
Remove the chicken from the grill after it's cooked through and transfer to a plate. Toast the brioche buns and then assemble the sandwiches with extra mayo (if desired) sliced tomato, the chicken, and slaw.