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Put the eggs into a pan of cold water, bring to a boil, then simmer for 8 mins. Put the beans into a steamer or heatproof colander, cover and steam over the egg pan for 4-5 mins or until just tender and very bright green. Meanwhile, whisk the dressing ingredients together and season with salt and pepper. Cool the eggs under cold water, then peel.
Heat a frying pan and add the oil. When hot, tip in the breadcrumbs and whole garlic clove. Stir for about 3 mins until toasty and golden, and just infused with the garlic. Chop the eggs, chives and anchovies and mix together.
Toss the beans with the dressing while still warm, then scoop onto a serving dish. Top with the anchovy mix and the crumbs, then spoon over any dressing left in the bowl.