Prepare spicy mayo: Mix garlic, mayonnaise and hot sauce in a small bowl. Cover and chill.
Prepare slaw: Toss onion, jalapeno, cabbage, pickles and pickle juice in a large bowl to combine. (additional juice may be added if the mixture seems too dry.) Cover and chill.
Prepare fried chicken: Whisk flour with black and cayenne peppers and salt in a shallow bowl. Pour buttermilk into another shallow bowl. Working with 1 piece at a time, dredge chicken in flour mixture, shaking off excess. Dip in buttermilk, allowing excess to drip back into bowl. Dredge again in flour mixture, shaking off excess.
Pour oil into a large heavy skillet to depth of 1/2 inch. Heat oil to 350 degrees.
Fry chicken until golden brown and cooked through, about 3 minutes per side. Transfer to wire rack set inside a baking dish; season with salt.
Assemble sandwiches: Spread cut sides of rolls with butter. Heat buttered sides in hot pan until browned and crisp, about 1 minute. Spread with spicy mayo. Build sandwiches with rolls, chicken and cabbage slaw.