Cut the salt cod into chunks and put them in a large bowl. Add enough water to cover. Let the cod soak, refrigerated, for 48 hours, replacing the soaking water with fresh water at least four times a day.
Bring a large pot of water to a boil and then reduce the heat so that the water is simmering. Add the cod and cover tightly. Turn off the heat and let the cod sit until the fish can be pulled apart with a fork or your fingers but is still moist, 10 to 15 minutes. Remove the fish from the water. When cool enough to handle, remove any bones and break up the fish.
Put the fish in a food processor and process until uniformly mashed. Add 2 of the eggs and process until well incorporated and the mixture is fluffy. Transfer the mixture to a bowl and stir in the parsley, garlic, onion, cumin seeds, mayonnaise, cayenne, salt, and pepper. Gradually add 1/3- to 1/2-cup of the breadcrumbs and mix them in; stop adding when the mixture is stiff.
Moisten your hands and shape the fish mixture into small disks (like hockey pucks) about 2-1/2 inches wide and 1 inch thick. In a bowl, beat the remaining 2 eggs; put the flour on one piece of waxed paper and the remaining breadcrumbs on another. Dredge the disks in the flour, dip in the beaten egg, and roll in the breadcrumbs. Set on a plate and refrigerate for 30 minutes.
Heat the oil in a deep-fryer or a deep stockpot to 375°F. Deep-fry the fritters, a few at a time, until deep golden brown, 2 to 3 minutes. Bring the oil back to 375°F before frying each batch. (If the oil is too hot, the fritters will darken very quickly without getting quite hot enough all the way through; if too cool, they'll absorb too much oil.) Drain the fritters on paper towels. Serve with tomato sauce, mayonnaise or aïoli, if you like.