Combine 3 cups shredded rotisserie chicken in a large bowl with diced celery, hot pepper sauce, white vinegar, cayenne pepper and 1/4 tsp garlic salt. Mix until combined.
Take the dinner rolls and slice with a serrated knife through the middle so as to halve all of the 12 rolls at once into a bottom and a top layer.
Place the bottoms of the rolls in a 9 x 13 oven safe baking dish and then put all of the chicken mixture over the bottoms of the rolls and spread evenly to the edges.
Place the cheese slices evenly on top of the chicken mixture then place the rolls tops on top of the cheese.
Next, combine the melted butter and the remaining 1/4 tsp garlic salt in a small bowl and then brush the tops of the rolls with the butter evenly.
Cover the sliders with aluminum foil and place in the oven for 20 minutes until the cheese melts. Then remove the foil and continue to bake another 10 minutes until the tops of the rolls are toasty browned.