Add chicken, red onion, ¼ cup of Frank's, blue cheese, salt and pepper in a bowl with hands, gently mixing until all ingredients have combined.
Melt 1 tablespoon of butter, and add 1/4 cup of Frank's. Pour this into the bowl in small batches with the celery and carrots, mixing as you go. You don't want this to be too soggy, but you want it to be dressed. Add a bit of salt and pepper to taste. This is a personal preference, so add more sauce or less. Let this sit to marinate in the flavour until the burgers are done.
Grill the burgers until done. We had them on a bed of lettuce, but obviously, a bun works – I mean, it's a burger. Pile that slaw on top of the burger and enjoy!