At least 24 hours ahead of time, put the baccalà into a large basin with enough water to cover them amply. Change the water from time to time. About halfway through, when the baccalà is already pliable, cut it into long, slender fillets, perhaps about 7-8 cm/3 inches long and 4 cm/1-1/2 inches wide or so. This will speed up the process of softening and de-salting the fish (see Notes below).

At least 2 hours ahead, whisk together in a large bowl the flour and enough mineral water so you have a smooth, silky, liquid but fairly thick batter (about the consistency of a pancake batter, if you're familiar with that.) Let it rest until you're ready to cook.

Heat up a deep skillet with enough olive oil in to come up at least halfway up the side. Drain the salt cod fillets and pat them dry. Then, when the oil is hot enough, but not smoking hot. dip each fillet in the batter, then into the oil. Keep adding fillets but make sure not to crowd the skillet too much. Fry at a moderate heat, turning from time to time, until the fillets are golden brown on all sides. This should take about 10 minutes or so, but no more.

As your fillets are done frying, drain them on paper towels or on a baking rack. Serve them as soon as they're all done, with lemon wedges if you like, and a light sprinkling of salt.