Combine cabbage, onion, carrots, and jalapeno peppers together in a bowl.
Blend egg, lemon juice, white vinegar, and salt in a food processor until smooth. Slowly drizzle oil into egg mixture through the feeding tube while the food processor is running until mayonnaise is smooth and thickened.
Mix mustard, sugar, cider vinegar, chipotle chile pepper, and celery salt into mayonnaise until dressing is smooth and evenly combined.
Stir dressing into cabbage mixture until evenly coated. Cover bowl with plastic wrap and refrigerate until flavors blend, at least 2 hours.
Shred cabbage and carrots using a food processor with the shredding attachment.
You can substitute 2 cups prepared mayonnaise instead of making your own.
This recipe contains raw eggs. We recommend that pregnant women, young children, the elderly, and the infirm do not consume raw eggs. Learn more about egg safety from our article, Making Your Eggs Safe.