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1
Lay the filleted anchovies in a shallow dish, cover with milk, and leave for 15 minutes. Lift out, rinse briefly under cold water, and pat thoroughly dry with kitchen paper. The fillets should smell clean and briny, without sharpness.
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2
Place the crushed garlic in the marble mortar. Pound steadily with the wooden pestle until the cloves collapse into a coarse paste. Add the anchovy fillets a few at a time, continuing to pound and work the pestle in a circular motion. This is where the dish lives or dies: the pounding must rupture the flesh fully to release the anchovy's flavour compounds, yet stop short of a smooth purée — the finished paste must show visible flecks of fish and garlic throughout.
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3
With the pestle still working, begin adding the olive oil in a thin, slow stream — a few drops at a time at first, exactly as for a mayonnaise. The paste will gradually take up the oil and thicken into a cohesive emulsion. Continue until all the oil is incorporated. The correct consistency holds its shape on the tip of a crudité without dripping.
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4
Add the tablespoon of red wine vinegar and a grind of black pepper. Pound and fold briefly to integrate. Taste: the anchovy should dominate, the garlic should be present but not overwhelming, and the vinegar should cut through the richness without announcing itself. Adjust pepper only.
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5
Arrange the chilled crudités on crushed ice in a Provençal terracotta bowl or on a cold platter. Set the mortar — still holding the anchoïade — at the centre. Serve immediately: the contrast between cold vegetables and room-temperature paste is deliberate.