Shred cabbage, onion, and carrot in food processor. Place in bowl and sprinkle 3/4 cup sugar on top of vegetables. Allow to set for 1 hour.
In a saucepan, bring vinegar, oil, and 2 tbs sugar to a boil, then pour over vegetables and allow to cool. Let mixture marinate at least 3 hours. Can be stored in refrigerator for several weeks.
Cajun Country -- New Iberia, Louisiana