Step 1Place the potatoes in a pot and add 1 teaspoon salt and cold water to cover. Cover, bring to a boil and cook until easily pierced.
Step 2While the potatoes cook, heat the oven to 400 degrees. Toss the shiitakes with 1 tablespoon of the oil and salt and pepper to taste. Spread on a baking sheet and roast 10 minutes, stirring occasionally. Remove from the oven and cool, then cut each one in half.
Step 3To make the dressing, combine the vinegar, lemon juice and mustard in a bowl and blend well. Whisk in the remaining 2 tablespoons olive oil, then the mayonnaise, until smooth. Add the sugar and anchovies and blend well. Season with salt and pepper to taste.
Step 4When the potatoes are cooked, drain well and dry. Cut each into quarters and place in a large shallow bowl. Add the shiitakes, cucumber and onions and toss to mix, then add the dressing and mix well. Let stand 15 minutes. Just before serving, add the watercress and toss to mix well.