Toss the cabbage and carrot with 1 tsp salt in a colander and let them drain over a bowl for 20 minutes.
Rinse the vegetables briefly under cold water, then spin them dry or press them firmly between clean towels.
Whisk the mayonnaise, vinegar, sugar, milk, celery seed, pepper and remaining 1/2 tsp salt until the sugar dissolves.
Fold the dry cabbage and carrot through the dressing until evenly coated.
Cover and refrigerate for 1 hour so the flavors settle, then stir and serve within 8 hours for the best crunch.