To make the vinaigrette, put the olive oil, vinegar, mustard, and shallot into a bowl and whisk together.
To make the leeks, bring a large saucepan of salted water to a boil. Carefully drop in the leeks and simmer over medium heat for about 15 minutes, until tender and easily pierced with the tip of a knife. Drain the leeks and pat dry with paper towels. Slice the leeks in half lengthwise.
Arrange the leeks on a serving plate and pour over the vinaigrette. Garnish with parsley and walnuts and season to taste with salt and freshly ground black pepper. Serve with baked or boiled potatoes.