1. Combine 1/4 cup vinegar, oil, Dijon mustard, and pepper in medium glass or metal bowl. Place bowl in freezer until vinegar mixture is well chilled, at least 15 minutes and up to 30 minutes.

2. While mixture chills, toss cabbage with 1/4 cup sugar and 1 teaspoon salt in large microwave-safe bowl. Cover with large plate and microwave on high power for 1 minute. Stir briefly, recover, and continue to microwave on high power until cabbage is partially wilted and has reduced in volume by ¬one-third, 30 to 60 seconds longer.

3. Transfer cabbage to salad spinner and spin cabbage until excess water is removed, 10 to 20 seconds. Remove bowl from freezer, add cabbage, Granny Smith apple, and tarragon to cold vinegar mixture, and toss to combine. If desired, adjust flavor with sugar or vinegar. Season with salt to taste. Refrigerate until chilled, about 15 minutes. Toss again before serving.