Toss shredded cabbage and carrots with 1 teaspoon salt in colander set over a medium bowl.
Let stand until wilted, about 1 hour.
Rinse cabbage and carrots under cold water, drain, dry well with paper towels, and transfer to a large bowl.
Stir in remaining ingredients plus salt to taste.
Refrigerate until chilled, about 15 minutes.
Adjust seasonings and serve.