For the fried fish: Add the eggs to a shallow baking dish and sprinkle with salt and pepper. Pulse the crackers to a powder in a food processor; spread out on a plate. On a separate plate, spread the panko and sprinkle with salt and pepper. Dip the fish pieces first in the egg, then in the crackers, back into the egg and, finally, into the panko. As you finish with each piece, place the breaded fish on a wire rack set into a baking sheet. Wrap tightly in plastic wrap and refrigerate for 4 to 5 hours.
Add 2 to 3 inches of peanut oil to a large, heavy pot set over medium-high heat. Heat the oil to 350 degrees F. In batches, fry the fish until cooked through and golden, about 4 minutes. Drain the fish on a wire rack and season with salt.
For the garlic butter bread: Mix together the butter, garlic, salt and pepper until well blended; butter the insides of potato buns with the mixture. Toast the buns until golden.
Set the fried fish in a roasting pan and top each piece with a slice of American cheese. Run under the broiler for 30 to 40 seconds, just until the cheese has melted.
To assemble, smear the insides of the buns with some Tartar Slaw, and add the fish. Serve with extra slaw on the side.
Grate the onion and pickles on a box grater. Transfer to a strainer and squeeze out excess moisture. Combine the grated onions and pickles in a large mixing bowl with the mayonnaise, mustard and cayenne. Mix well and season with salt and pepper. Refrigerate, covered, until ready to use.