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1
The day before, submerge the salt cod in cold water and refrigerate, changing the water several times over 24 hours. The fish is sufficiently desalinated when a small piece tasted raw is pleasantly saline rather than sharp.
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2
Pound the garlic cloves and coarse salt together in the marble mortar in a slow, steady rotation until every trace of fibre has disappeared and the paste is perfectly smooth and white. Add the boiled potato and continue pounding until fully incorporated. No garlic chunk should remain — any coarseness here will prevent proper emulsification and the dish will not hold.
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3
Add the egg yolks to the garlic paste and stir them in with the pestle until the mixture is uniform and slightly paler. This is where the dish lives or dies: begin adding olive oil one drop at a time, working the pestle in continuous slow circles, watching the mass thicken and bind before each addition. Once a firm emulsion is clearly established — the paste pulls away from the mortar wall and holds its shape — increase the oil to the thinnest possible stream, never faster. The finished aïoli should be so thick that a spoon stands upright in it.
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4
Cook each accompaniment separately. Boil the potatoes whole in well-salted water; they are done when a skewer meets firm, waxy resistance — not floury collapse. Steam the carrots until a knife tip enters without force but the carrot does not bend. Steam the green beans until the colour deepens to vivid green and each bean snaps cleanly. Steam the artichokes whole until an outer leaf pulls free with gentle resistance.
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5
Poach the drained salt cod in water held at 70 °C — never a full boil. The fish is done when it flakes readily into large, moist, pearlescent layers when pressed lightly with a finger; it must not be allowed to tighten or shred.
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6
Allow all components — fish, vegetables, eggs, chickpeas — to cool fully to room temperature before arranging on communal platters. Room temperature is not a convenience but a condition: cold suppresses the flavour of the garlic emulsion; heat alters its texture. The scent of the aïoli should be powerfully pungent at the table — assertive garlic and olive oil, with no raw sharpness.
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7
Set the mortar at the exact centre of the table. Arrange the salt cod, eggs, potatoes, carrots, beans, artichokes, and chickpeas on wide platters around it. Each diner dips directly from the communal mortar — the social act of sharing a single vessel is as constitutive of the dish as any ingredient.