Mayonnaise ,Mix garlic, and hot pepper sauce in a little bowl; cover and chill. Toss onion, jalapeño, cabbage, pickles, and pickle juice in a big bowl to combine; cover and chill.
FRIED CHICKEN STEPS:
- Whisk flour, pepper, and 1/2 teaspoons salt in a shallow bowl. Pour buttermilk into some other 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-inch. Prop deep-fry thermometer in oil so bulb is submerged. Heat over medium heat until thermometer registers 350°.
- 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 bowls, chicken, and cabbage slaw.