Cut the pork crosswise into 4 equal pieces. Put each piece flat on a cutting board and slice horizontally almost in half (stop about 1 inch from the other side). Open like a book. Sprinkle each piece with water, place between 2 pieces of heavy-duty plastic wrap and pound to 1/4 inch thick with a mallet or heavy skillet.
Whisk the eggs, buttermilk, garlic, 1 teaspoon each salt and black pepper, and the cayenne in a shallow bowl. Add the pork, cover and refrigerate at least 4 hours or overnight.
Pulse the crackers into coarse crumbs in a food processor, then transfer to a shallow dish. Put the flour in another dish. Remove each piece of pork from the marinade, letting the excess drip off. Dredge both sides in the flour, dip in the buttermilk marinade again, then coat with the cracker crumbs.
Heat 1/4 to 1/2 inch peanut oil in a large heavy-bottomed skillet over medium-high heat until a deep-fry thermometer registers 360. Fry the pork in batches until golden and cooked through, about 3 minutes per side. Drain on paper towels.
Spread both halves of each bun with mayonnaise and mustard. Layer the lettuce, tomatoes and onion on the bottom halves. Add a piece of pork and a few pickle slices. Cover with the bun tops.