Whisk buttermilk, salt, hot sauce, and ranch dressing mix together in a large bowl. Cut diagonal slits into the thick ends of chicken breasts and toss into marinade until well coated. Transfer to the refrigerator to marinate for 2 to 4 hours.

Meanwhile, make the breading: Mix flour, cornstarch, salt, pepper, cayenne, and ranch dressing mix together in a shallow dish.

Make the wash: Whisk egg, buttermilk, and milk together in another bowl until combined.

Use a fork to pull chicken from marinade, letting any excess drip off. Dip into the breading to coat both sides; shake off any excess. Dip into egg wash mixture to saturate surface; return to breading to coat, shake off excess, and repeat once more. Let sit on a wire rack to dry, at least 15 minutes.

Heat oil in a deep-fryer to between 350 degrees F (175 degrees C) and 375 degrees F (190 degrees C).

Fry chicken breasts in the hot oil until golden, crispy, and no longer pink in the centers, 4 to 5 minutes, flipping halfway through. Transfer to a plate topped with crinkled up aluminum foil to prevent bottoms from getting soggy.

Spread mayonnaise over hamburger bun halves. Stuff with pickles and chicken.