Blanch the mushrooms in boiling water for about 2 minutes. Remove from the water and drain, stem-side down, while you prepare the filling.
Remove tough green leaves from the leek. Trim the root end and slice the leek in half lengthwise. Rinse well to remove any grit from between the layers. Mince.
In a small bowl, mix the leeks, cottage cheese and mustard. In another small bowl, beat the egg white until stiff peaks form. Fold into the cottage cheese mixture. Spoon the filling into the mushroom caps. Sprinkle with paprika.
Bake at 400 degrees F until the filling is set, about 20 minutes.