Add the buttermilk, hot sauce, kosher salt, and white pepper to a small mixing bowl. Whisk the marinade to combine.
Place the chicken in either a sealable container or a gallon-size ziplock bag. Pour the marinade over the chicken. If you are using the container, turn the chicken over to coat completely. If using the ziplock, tightly seal the bag and “massage” the chicken to completely coat the chicken. Place in the refrigerator for at least 4 hours or overnight.
Add the mayonnaise, ketchup, and sriracha to a small bowl. Whisk to thoroughly incorporate. Cover and chill in the refrigerator until ready for garnishing the sandwiches.
Just before frying the chicken, Add the self-rising flour, onion powder, kosher salt, white pepper, paprika, and cayenne pepper to a shallow bowl or baking dish. Whisk to combine and set it aside.
Add the oil to a 4 to 5-quart stock pot. Heat the oil over medium-high to high heat. You will want to use a candy/deep frying thermometer to help you monitor the temperature. Heat the oil to 330 to 350°F. We find 340°F seems to be the sweet spot.
Just before the oil reaches 325°F, remove 1 piece of chicken at a time from the marinade. Allow some of the marinade to drip off. Dredge the coated chicken in the flour mixture.
Immediately add the coated chicken to the heated oil. You should be able to cook 2 pieces of chicken at a time. Keep a close eye on the temperature, adjusting the stove top temperature up and down to keep the oil at the appropriate temperature. Keep in mind that the oil temperature will fluctuate when you add the chicken. Fry the chicken for 5 to 7 minutes per side.
Once the chicken is a deep golden brown and the internal temperature reaches 165°F, remove the chicken to a baking dish lined with paper towels. Repeat the steps for the remaining 2 pieces of chicken.
While the first batch of chicken is draining, lay 2 slices of muenster cheese over the hot chicken.
Once all the chicken pieces have been cooked and the cheese has been added, spread the zinger sauce on the top bun. Place the chicken on the bottom bun and top with iceberg lettuce. Top with the bun and serve.