Trim dark green tops of leeks so that only a tiny part of the green remains. Leave slightly trimmed root attached to keep leeks held together.
Bring a large pot of salted water to a steady boil. Add leeks and simmer, covered, for 10 to 12 minutes. Leeks should be tender and cooked through. Remove from water with tongs and place in an ice bath. Place eggs in the same boiling water and cook for 10 minutes, until hard-boiled. Remove with tongs and let cool. Chop eggs and reserve for garnish.
When leeks are cooled, slice in half lengthwise without cutting all the way through. Remove outer part of leeks. Pull top green part of leeks apart and rinse out any grit under cold water. Drain leeks and chill for 2 hours. If a quick chill is needed, leeks can be placed in the freezer for 20 to 30 minutes.
in a small, nonreactive mixing bowl, combine sun-dried tomatoes, vinegar, mustard, salt, pepper, capers, and green olives. Drizzle oil into bowl while whisking thoroughly. Season to taste. Adjust balance of vinaigrette if necessary. Refrigerate.
To serve, divide leeks evenly on chilled plates, fanning out leaves slightly and leaving them attached to the root. Whisk vinaigrette thoroughly and drizzle over top of leeks. Any remaining vinaigrette can be used as a topping for seafood or salad. Garnish with chopped hard-boiled egg.