Cook the new potatoes for 10-15 minutes until tender then drain in a colander. Whilst the potatoes are cooking, cook the broad beans in boiling salted water until just tender, then drain. Half the new potatoes then mix in a bowl with the broad beans, most of the olive oil, capers, parsley and lemon juice and season with salt and pepper. Cover the bowl with Clingfilm to keep warm.
Bring a pan of water to the boil and cook the duck eggs for 4 ½ minute for normal sized ones or 5-6 if they are really large. Carefully drain and rinse under the cold tap for a minute or so to cool them a little then carefully remove the shells. Arrange the potato mixture onto serving plates or bowls and break an egg in half into the centre of each. You can leave them whole if you wish. Drizzle with more olive oil and serve immediately.