Cook the potatoes in lightly salted boiling water, leave them to cool and halve them. Meanwhile, bring a large saucepan of lightly salted water to the boil, add the trimmed green beans and blanch for 1—2 minutes until bright green and still firm to the touch. Refresh in cold water, drain and transfer to a large salad bowl.
Core the tomatoes and cut each one into 6 pieces. Add the tomatoes and chopped parsley to the beans with the potatoes, olives, lemon juice and oil. Season to taste with salt and pepper.
Transfer the salad to serving plates and top each one with a poached egg cut in half and a drizzle of olive oil. Garnish with the reserved parsley leaves and serve.