In a large bowl, toss together the cabbage, carrots and onion. Set aside.
Place the egg yolks, mustard powder and vinegar in a food processor and blend. While the motor is running, drizzle the oil very slowly through the lid, incorporating each drop before adding more. Continue adding the oil until the mayonnaise reaches the desired consistency, adding a little warm water if it becomes too thick. Add more mustard powder or vinegar to taste and season with white pepper. Stir half the mayonnaise through the vegetables and mix together well.