Whisk vinegar and mustard in medium bowl. Gradually whisk in oil. Stir in garlic, thyme, and basil. Season to taste with salt and pepper. DO AHEAD: Dressing can be made 1 day ahead. Cover and chill.
Preheat oven to 450°F. Toss onions and next 6 ingredients in large bowl; sprinkle with coarse salt and pepper. Add dressing; toss to coat. Divide between 2 large rimmed baking sheets. Roast until vegetables are tender and slightly brown around edges, about 35 minutes.