Spray grill rack with nonstick spray.
Prepare barbecue grill (medium-high heat).
Whisk vinegar, sugar, 1/2 cup oil, mustard and tarragon in medium bowl. Season dressing with salt and pepper.
Brush cabbages and green onions with oil; sprinkle with salt and pepper. Grill cabbages until dark grill marks form, 3 - 4 minutes per side. Grill green onions until charred on one side, 2 - 3 minutes. Transfer vegetables to work surface.
Chop green onions and cabbages; place in large bowl, discarding cores. Add dressing, toss to coat. Season slaw to taste with salt and papper.
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