Cook the green beans in boiling salted water for three minutes or until just tender, then drain and refresh under cold running water. Dry on kitchen paper and set aside.
Cut the tomatoes in half and place in a bowl. Add the green beans. Whisk together the olive oil and vinegar with a little salt and pepper and pour over the beans and tomatoes.
Heat a little water in a pan and crack the eggs, two at a time, into the water. Poach for three minutes to give a soft centre. Remove from the water with a slotted spoon and drain on kitchen paper. Repeat for the remaining eggs. Portion out the beans and tomatoes onto plates and top each one with a poached egg. The runny yolk will help create a dressing.