Slice eggs in half crosswise. Separate the whites from the yolks. Slice the egg whites into ringlets and set aside.
In a bowl, whisk together the yolks and cold water until the yolks are dissolved. Whisk in the oil, salt, sugar, and mustard until combined well. Add the vinegars.
Toss the greens with the dressing. Transfer to a serving bowl. Place scallions around the outside and top with the egg white ringlets.