Place the eggs into a pan of boiling water. Boil for eight minutes exactly, then drain and cool under cold running water. Peel the eggs and set them aside.
Trim the very tops off the leeks and then cut two-thirds of the way down. Discard any of the coarse outer leaves of the upper two-thirds, cut in half lengthways and horizontally and separate the inner green stems into strips.
Cut the lower white part of the leek into rounds. Steam the white round and green strips in a steamer placed over salted boiling water for four minutes, or until tender.
Run the leeks under cold water to cool. Squeeze them out if they are at all watery.
Meanwhile, heat a small frying pan and add a tablespoon of the oil. Once hot, add the sliced mushrooms to the pan with a pinch of salt. Cook over a medium heat for 4-5 minutes, or until tender and lightly golden-brown. Add the garlic and fry for another minute.
Whisk the remaining olive oil together with the vinegar and mustard in a small bowl to make a dressing. Taste and season as necessary. Cut the peeled eggs into wedges. Put the cooled leeks in a bowl and top them with the eggs. Season with salt and pepper
Dress the egg and leek with the dressing. Taste and adjust the seasoning if needed. Serve with the mushrooms and baguette.