Place the anchovies and garlic on a clean chopping board and sprinkle over a small pinch of coarse salt. Use the edge of a knife to scrape and mash the ingredients together to form a rough paste.
Place the anchovy paste into a bowl and add the Parmesan, oil and mayonnaise. Grate in the lemon zest then squeeze in the lemon juice and stir all the ingredients well to combine.
Add 1–2 tablespoons of ice-cold water, depending on your desired consistency, and stir to loosen. Season to taste with salt and freshly cracked black pepper. Kept in the fridge in a sealed container, this dressing will stay fresh for 3–5 days.
