Thinly shred the green cabbage using a sharp knife or food processor, then place it in a large mixing bowl.
Peel and grate the carrot, then add it to the bowl with the cabbage for a vibrant mix of textures and colors.
In a separate small bowl, whisk together mayonnaise, white vinegar, sugar, salt, and black pepper until smooth and well combined.
Pour the creamy dressing over the shredded cabbage and carrots, then toss gently to evenly coat all the vegetables.
Continue tossing until the mixture is uniformly coated and the cabbage begins to soften slightly, about 1–2 minutes.
Transfer the coleslaw to a serving dish and let it rest for at least 10 minutes to allow flavors to meld and the texture to improve.
Serve the creamy coleslaw chilled, garnished with extra black pepper or fresh herbs if desired, alongside your favorite main dishes.