In a large bowl, soak the chicken livers in 1/2 cup of the buttermilk for 1 hour.
Meanwhile, to prepare for breading the livers, mix the flour, salt, black pepper, and cayenne in a large plastic food-storage bag. In a bowl, whisk together the eggs with the remaining 1 cup of buttermilk. Place the saltine crumbs on a plate.
Once the livers have soaked, drain them (discarding the soaking buttermilk) then lightly season them with salt and pepper. Place the chicken livers in the flour bag and shake until they are well coated. In batches, dip the flour-coated livers into the eggs and then lightly dredge in the saltine crumbs. Place cracker-coated livers on a large plate or sheet. Repeat until all the livers are coated.
In a large cast-iron skillet, heat 1/2 inch of oil on medium-high heat until it reaches 350°F, about 5 minutes. If you don’t have a thermometer, you can test the temperature by sticking a wooden spoon into the oil. If it bubbles around the spoon, it should be ready for frying. Line a sheet pan with paper towels.
Fry the livers for 5 minutes or until brown and crisp, turning once. (When you place the livers into the skillet, be careful, as there may be excessive popping of the oil.) Depending on the size of your skillet will probably have to fry them in several batches. Drain on paper towels. Serve warm with cream gravy.
While I like to keep it simple, adding other spices and herbs to the flour mixture, such as sage, garlic powder, and chili powder, are also very good