To make the dressing, mash the garlic and anchovy, if using, with a small pinch of salt on a board using the blade of a large knife, or in a pestle and mortar. Combine the paste with the mustard and vinegar, then slowly stir in the tuna oil. Set aside.
Tip the new potatoes into a large pan of cold salted water, ensuring they’re well covered. Bring to the boil, then reduce the heat to a simmer. Add the beans and cook for 5 mins, then remove with a slotted spoon and immediately plunge into a bowl of iced water to cool. Cook the potatoes for another 5 mins until tender, then drain and leave to cool. When cool enough to handle, halve or quarter them, and toss in a large bowl with 1 tbsp of the dressing. Leave to cool completely.
Meanwhile, cook the eggs in a second pan of simmering water for 7½ mins, then transfer to a bowl of iced water to cool. Drain the beans and eggs, then peel and halve the eggs.
Tip the lettuce quarters, cooked beans and olives into the bowl with the potatoes. Add most of the remaining dressing and gently toss. Divide the salad between two bowls, and top with the tomatoes and eggs. Flake over the tuna, then drizzle with the rest of the dressing and season.