Place the barley in a small saucepan and cover with the water. Bring to a boil, cover, and reduce to a simmer and cook for 45 minutes to 1 hour, or until the barley is tender. Drain any excess water.
Meanwhile, place the dried mushrooms in a small bowl and cover with boiling water and leave for 20 minutes to soak.
Place a large frying pan over a medium heat and add the butter or olive oil along with the leek. Cook until softened and slightly caramelised. Remove from the pan. Add the mushrooms and cook until tender and slightly caramelised. Remove from the pan. Add the dried mushrooms and enoki to the pan along with half the soaking liquid. Cook for 3 to 4 minutes, or until the soaking liquid is absorbed. Add the mushrooms, leek and barley to a bowl, along with salt and pepper, and toss to combine.
Whisk the red wine vinegar, extra virgin olive oil and mustard in a small bowl and add to the mushroom and barley mixture. Toss well and check the seasoning. Finally, add the watercress. Divide between 2 plates or bowls.
Fill a large frying pan with 1 ½ inches of water. Heat over medium heat just until bubbles appear on bottom add the vinegar. Break one egg and carefully and slowly lower the egg into the water. Repeat with the second egg. Cook until whites are just firm, around 4 to 6 minutes. Remove with a slotted spoon and drain on paper towels. Place on top of the salad and serve immediately.