Place a rack on the upper third of your oven and turn the broiler to high. If you haven't already, shred enough chicken to fill 2 cups, chop enough pickles to fill 1/2 cup and dice 2 dates.
In a large bowl, combine shredded chicken, chopped pickles, diced dates, 1 tbsp dijon, 2 tbsp pickle brine, 1/3 cup greek yogurt and 3 tbsp mayonnaise. Mix until well incorporated. Taste and adjust seasoning, it should be creamy and pickle-y.
Heat an oven-safe pan on high heat. Spread a thin layer of mayonnaise on either side of the buns and place them face down in the pan. Toast your buns until they are golden brown. You might have to work in batches depending on the size of your pan.
Remove the tops and arrange the bottoms in the pan. Scoop chicken salad onto the bottoms (about 1/2 cup per sandwich) and top with shredded cheese. Place under the broiler and cook for 1-2 minutes, or until the cheese starts to bubble and brown. Remove and serve with more dill pickles and chips.
