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1
Place the salt-packed anchovies in a bowl of cold water and soak for 30 minutes. Lift them out, rinse, and fillet carefully. Taste a single fillet: it should be savoury and complex, not sharp or metallic. If still aggressively salty, soak a further 10 minutes. The dish is decided here — under-desalted anchovies will make the finished tortino unbearable.
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2
Peel the potatoes and slice them to exactly 2 mm on a mandoline. Hold the slices in cold water until needed, then drain and pat dry. A slice held to the light should be almost translucent.
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3
Lightly oil the base of a baking dish. Lay down a single, slightly overlapping layer of potato slices. Arrange anchovy fillets evenly across the potato, then place tomato slices sparingly over the anchovies — tomato is a background element, not a dominant one. Scatter olives if using. Drizzle with olive oil. Repeat the layering sequence — potato, anchovy, tomato, oil — until all ingredients are used. Finish with a top layer of potato slices and a final drizzle of olive oil. The assembled dish should show distinct, even strata with no pooling liquid.
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4
Cover the dish tightly with foil and bake at 180 °C for 30 minutes. The dish is ready for uncovering when the kitchen carries a deep, savoury-sweet anchovy aroma and the foil has begun to dome slightly from internal steam.
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5
Remove the foil and return the dish to the oven for a further 15 minutes. The tortino is done when the top layer of potato is golden and beginning to crisp at the edges, and a skewer passes through all layers without resistance — the potatoes must be fully yielding.
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6
Rest the tortino for 5 minutes out of the oven. Scatter fresh flat-leaf parsley over the surface — parsley added before baking loses all freshness. Serve directly from the dish; the rendered anchovy-olive oil pooled at the base should be offered with crusty bread.