Cut tofu slab in half horizontally to split. Cut each piece in half crosswise to make 4 (2¼- x 3¼- x ¾-inch) slabs. Place tofu slabs in an even layer in an airtight container. Cover and freeze 12 hours. Transfer tofu to refrigerator, and let thaw 12 hours. Wrap tofu slabs in a clean kitchen towel, and press down on tofu to remove any excess liquid. Pour pickle juice into a shallow dish. Add tofu slabs, and let soak 10 minutes, flipping tofu slabs once after 5 minutes.

Stir together hot sauce and mustard in a small bowl; set aside. Stir together flour, cornstarch, black pepper, salt, paprika, garlic powder, and crushed red pepper in a separate shallow bowl. Pour oil into a large, heavy skillet to a depth of ¼ inch; heat oil over medium-high until oil is gently rippling or reaches 350°F.

Remove tofu from pickle juice, and pat dry; discard pickle juice. Working with 1 tofu slab at a time, dredge tofu in flour mixture, gently pressing to adhere. Tap tofu against bowl to shake off excess; transfer to a plate.

Working with 1 floured tofu slab at a time, lightly brush hot sauce mixture all over tofu. Re-dredge tofu in flour mixture, gently pressing to adhere. Tap tofu against bowl to shake off excess; transfer to a plate.

Carefully add tofu slabs to hot oil; fry until crispy and golden brown, 5 to 7 minutes, using tongs to flip tofu halfway through cook time. Remove fried tofu from skillet, and place on a wire rack set inside a rimmed baking sheet. Immediately sprinkle tofu with salt to taste.

Serve tofu on hamburger buns with spicy mayonnaise, pickles, cabbage, and hot sauce.