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Under cold running water, scale and gut the anchovies, removing the gills, but leaving the head and tail intact. Remove the fins. Open the body cavity, and using your thumbnail, loosen the meat of the fish from the spine. Gently remove the spine by twisting or cutting it off a the base of the anchovy's head and tail.
Grill the anchovies over a hot charcoal fire, skin side down for about 2 minutes, or until the flesh of the fish becomes white. Transfer to a large serving platter, arranging the anchovies skin side up on the platter. Squeeze a little lemon juice over the fish. Drizzle with olive oil and season with sea salt and pepper. Sprinkle the parsley and olives over the anchovies and serve immediately.