Remove the heads, guts, and backbone from the anchovies. Butterfly them and rinse under very cold water.
Place the cleaned anchovies in the freezer at 0°F (–18°C) or colder for 48–72 hours. Then thaw them slowly in the refrigerator.
Spread a layer of coarse salt over the thawed anchovies. Let them sit for 30 minutes, then rinse off the salt and pat the fillets dry with paper towels.
Arrange the anchovies skin-side up in a glass or plastic container.
In a bowl, mix the white wine vinegar and cold water. Pour the mixture over the anchovies until they are fully submerged. Cover and refrigerate for 6–8 hours or overnight.
Drain the anchovies in a colander, pressing gently to remove any excess liquid.
Finely chop the garlic and parsley.
Place the drained anchovies on a serving platter. Sprinkle the garlic and parsley over them, then drizzle generously with extra-virgin olive oil.
Let the anchovies marinate in the oil and seasonings for at least 30 minutes before serving. Serve with olives, potato chips, or bread, if desired.