Toss shredded cabbage with carrots and 1 tablespoon of kosher salt in a mesh colander set in a large bowl. Let stand for 1 hour.
Discard the water that collects in the bowl and dry the bowl. Rinse the cabbage and carrots, and dry well in a salad spinner, or between layers of paper towels on a baking sheet. Place the dried cabbage mixture back in the large bowl.
In a bowl, combine vinegar and sugar, stirring until the sugar is dissolved. Whisk in mayonnaise, celery seed, 1/4 teaspoon kosher salt, and 1/2 teaspoon freshly-ground black pepper.
Pour as much dressing over the cabbage and carrots as you like (you might not use it all depending on your personal preferences and how much moisture is left in your cabbage).** Season to taste with salt and pepper.
Cover and chill for at least 1 hour, stirring the coleslaw before serving. Coleslaw keeps, covered and refrigerated, for up to 3 days.
*As written, the dressing makes a lightly sweet and tart coleslaw. If you like your coleslaw a little less sweet, start by reducing both the sugar and vinegar to 2 tablespoons, adding additional, to taste.**I tend to vary my dressing quantity based on how I'm serving the coleslaw. If it's a side dish, I make it creamier and use all the dressing. If I'm using it to top sandwiches, like pulled pork, I'll use a little less.