Use a sharp chef's knife to thinly shred the green cabbage and peeled carrots; aim for fine, even strands that will crackle with each bite.
Place the shredded vegetables into a large mixing bowl, distributing them evenly.
In a separate small bowl, whisk together the mayonnaise, vinegar, sugar, and a pinch of salt and pepper until the dressing is smooth and slightly tangy.
Pour the dressing over the shredded cabbage and carrots, then gently toss everything together with a spatula or tongs, ensuring each strand is coated evenly.
Taste the slaw and adjust seasoning with more salt, pepper, or vinegar if desired for a balanced flavor.
Serve immediately for the crunchiest texture, or chill in the fridge for up to 2 hours to allow flavors to meld.