In a mixing bowl, combine the cucumbers and vinegar and toss gently until the cucumbers are well coated. Marinate at room temperature for 30 minutes, then drain the cucumbers through a large mixing bowl.
Separate the egg yolks from the whites of the hard-cooked eggs. Cut the whites into strips ⅛ inch wide and 1 to 2 inches long and set aside the egg whites.
With the back of a large spoon, rub the egg yolks through a fine sieve set over a small bowl. Slowly beat in the mustard, your cream, white wine vinegar, sugar and white pepper.
When the dressing is smooth, pour it over the cucumbers and toss together gently but thoroughly. Taste for seasoning.
To serve, arrange the lettuce leaves on a large flat serving plate or on small individual plates and mound the salad on top of them. Sprinkle with dill and refrigerate until ready to serve.