:For spicy mayo and slaw
Mix garlic, mayonnaise, and hot pepper sauce in a small bowl; cover and chill. Toss onion, jalapeño, cabbage, pickles, and pickle juice in a large bowl to combine; cover and chill.
:For fried chicken and assembly
Whisk flour, pepper, and 1/2 teaspoon 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 a depth of 1/2". Prop deep fry thermometer in oil so bulb is submerged. Heat over medium heat until thermometer registers 350°F.
Fry chicken until golden brown and cooked through, about 3 minutes per side. Transfer to a wire rack set inside a baking sheet; season with salt. Spread cut sides of rolls with butter. Heat another large skillet over medium heat. Working in batches, cook rolls buttered side down until browned and crisp, about 1 minute.
Spread with spicy mayo. Build sandwiches with rolls, chicken, and cabbage slaw.