Combine the eggs, oil, vinegar and mustard in a small saucepan.  Cook over medium heat, stirring constantly with a wire whisk.  When thick and smooth, remove from heat and set aside to cool.  Before blending with the salad, add the mayonnaise and stir well until incorporated.

Mince the onion and celery in the bowl of food processor with the blade in place.  Transfer to a large mixing bowl.  Remove the blade and insert the disc with the slicing edge.  In several batches, process the cabbage through the feed tube until all is shredded.  Empty contents into the mixing bowl with the onion and celery after each batch.

Using the coarse shred side of a box grater, grate the carrot by holding it on the diagonal producing longer shreds.  Add the carrot to the cabbage mixture.  Sprinkle the sugar, salt and pepper over the prepared vegetables and mix well.

Add the dressing to the cabbage mixture and stir well.  Chill several hours before serving.

NOTE:  If a creamier dressing is preferred, add additional mayonnaise until reaching the desired consistency.