To prepare coleslaw, in a large bowl, whisk together mayo, buttermilk, rice vinegar, sugar, lemon juice, celery salt, cayenne, and pepper until smooth. Add shredded cabbage and carrot and toss to coat. Refrigerate until ready to use.
For fried pickles, in a medium bowl whisk together flour, cornmeal, cayenne, pepper, and salt. Add ¾ cup buttermilk and stir until smooth. Add more buttermilk, 1 tablespoon at a time, until the consistency of thin pancake batter.
Drain pickles and arrange on a layer of paper towels; pat dry.
In a medium saucepan, add enough oil to a ¾-inch depth. Heat over medium heat until oil temperature registers 350 degrees F.
Dip pickle slices into batter and gently drop into hot oil. Repeat with 6-7 more pickle slices, frying in batches so as not to overload the pan. The pickles will stick together so you want enough space between them.
Fry for about 2 to 3 minutes, flipping once part-way through, until pickles are evenly golden brown. Remove with a slotted spoon and place on a paper towel-lined plate to drain.
To assemble sandwiches, lightly toast or warm rolls to soften. Spread bottoms with a thin layer of mustard. Top with approximately ⅓ cup of shredded chicken, a heaping ⅓ cup or so of coleslaw, and 4-5 fried pickles. Top with other half of roll and serve immediately.
