Trim most of the green and the thick outer layers from each leek. Trim any roots but leave them attached at the bottom.
Heat a large frying pan, with a lid, with enough water to cover the leeks. Add a vegetable stock cube and, once dissolved, add the leeks. Cover and simmer for 20-30 minutes until completely tender when you pierce them with a knife. Err on the side of soft – you don’t want chewy leeks!
While the leeks are cooking, make the vinaigrette. Whisk the dijon and vinegar then gradually whisk in the olive oil. Stir in the shallots and season.
Drain the leeks really well, then cut right down the middle while they’re still warm. Put them cut-side up in a dish, side-by-side, then spoon the vinaigrette over. Leave to cool to room temperature then serve with the egg, capers and parsley scattered over. You can make these ahead and chill them but let them come up to room temperature before adding the garnish and serving.