Boil the potatoes for 10-12 minutes until tender. Drain well then halve. Trim the beans then cook in boiling salted water for 2 minutes. Drain and refresh in iced water. Drain well once more and pat dry.
Mix the potatoes and beans with the tomatoes, olives, capers, anchovies and shallots. Whisk the ingredients for the vinaigrette and season with salt and pepper. Toss the tomatoes, olives, anchovies and capers in some of the vinaigrette. Place 3 of the larger gem lettuce leaves on each serving plate then divide the salad between them.
Heat a large non-stick frying pan until you can feel a good heat rising. Add 1 tbsp of the oil then lay in the tuna steaks. Cook for 1-2 minutes on each side until they feel slightly springy when pressed. The tuna should still be pink in the middle. Deglaze with the balsamic vinegar. Season and lift out of the pan. Cut each steak in half and place on top of the salad.
Place the eggs in to a pan of boiling water and cook for 6 minutes (for a well set white and runny yolk). Plunge the eggs into iced cold water to prevent them from cooking further. Once cooled, roll the egg on the work surface, gently applying pressure so the shell begins to crack, then peel off the shell.
Place the eggs on top of the tuna and cut in half, to reveal the soft runny yolk. Scatter with basil leaves then serve.
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