To make the dressing, microwave lime in a small bowl to release essential oils, and set aside until cool enough to handle. Through the feed opening of a running blender add, 1 at a time, the papaya, papaya seeds, Dijon mustard, vinegar, salt, pepper, and juice from the microwaved lime. (Note: If you squeeze the lime with the sliced side against your palm, the seeds are likely to stay in the rind.) Then with the blender still running, add the olive oil in a slow thin stream. Please note that the edible papaya seeds lend a wonderful mustard-y taste to the dressing, but are coarse in texture. If you find the texture to be too coarse for you, strain the dressing before use.
Toss the greens and cilantro with enough of the dressing to coat, serving additional dressing on the side.