Wash vegetables. Rinse the cabbage and carrot under cool water and pat dry. Removing excess moisture now helps prevent watery coleslaw later.

Thinly shred the cabbage. Cut in half, remove the core, and slice as thin as possible.

Grate the carrot. Peel first, then grate using a box grater or food processor. Add to the bowl with the cabbage.

Prepare the creamy dressing. In a small bowl, whisk together the mayonnaise, lemon juice, sugar, salt, and black pepper until smooth. Taste and adjust before adding to the cabbage.

Combine everything. Pour the dressing over the cabbage and carrots. Toss gently until every strand is coated, without overmixing.

Chill for 30 minutes. Cover and refrigerate before serving so the flavors settle and the cabbage softens slightly.