Place the green and purple cabbage in a large mixing bowl. Use a chef's knife or food processor to shred the vegetables into fine strips and grated carrots, then combine them thoroughly. Ensure the mixture is evenly shredded with vibrant colors and a slightly glossy appearance.
In a small bowl, whisk together mayonnaise, apple cider vinegar, sugar, salt, and black pepper until the dressing is smooth and well combined. Look for a creamy consistency with a slight tang and a glossy sheen, indicating proper emulsion.
0.5 cup mayonnaise, 2 tablespoons apple cider vinegar, 1 teaspoon sugar, 0.5 teaspoon salt, 0.25 teaspoon black pepper
Pour the dressing over the shredded vegetables. Use a spatula or large spoon to fold the mixture gently until all the vegetables are coated evenly and the dressing is distributed uniformly. The mixture should be well-glazed and vibrant, with the vegetables maintaining their crunch.
Cover the bowl with plastic wrap or a lid, and refrigerate for at least 30 minutes to allow flavors to meld and improve the texture. The coleslaw will become slightly softer, with a crisp, refreshing bite.
Remove the coleslaw from the refrigerator. Give it a gentle toss to redistribute the dressing. Transfer to a serving dish, and serve chilled with your favorite fried dishes or sandwiches. Garnish with additional black pepper or herbs if desired.