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1
Place the soaked, cleaned stockfish and the potato chunks in a large, heavy pot. Cover with cold unsalted water — no salt; the fish carries its own. Bring to a gentle simmer over medium heat. Cook until the potato is completely tender and beginning to fall apart, and the stockfish flakes readily at the touch of a fork — both yielding at the same moment is the mark of readiness.
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2
Drain thoroughly, reserving a ladleful of the cooking water. Return the fish and potato to the pot. Set the pot over the lowest possible heat to drive off any excess moisture — the surface of the mixture should look dry and faintly steaming, not pooled with liquid.
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3
This is where the dish lives or dies. Cover the pot with its tight-fitting lid. With one hand steadying the lid firmly, shake the pot vigorously in a circular motion while a second person — or a steady pause — pours the olive oil in a thin, continuous stream through the cracked lid. Continue shaking without pause, adding oil gradually; the mixture should swell, lighten in colour, and cohere into a rough, aerated mass. If the emulsion tightens too much, add a spoonful of the reserved cooking water. The finished texture is coarse and pillowy — it holds its shape on a spoon but is not smooth.
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4
Remove from the heat. Stir in the grated nutmeg and the finely chopped black olives. Taste and season with salt only now — cautiously, as residual salt from the fish varies. The flavour should be savoury and rounded, with the olive oil present but not dominant.
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5
Spoon onto the garlic-rubbed crostini and serve immediately. The brandacujun should be warm and just set; it stiffens as it cools. The contrast between the crisp bread and the silky, slightly chunky fish is the intended result.