Whisk vinegar, Dijon mustard, and 5 tablespoons oil in small bowl. Stir in cheese. Season dressing with salt and generous amount of pepper. Prepare barbecue (medium-high heat); brush grill with oil. Place all vegetables except beets, onion, and baby greens in large bowl; drizzle with remaining 4 tablespoons oil and toss to coat. Transfer to large rimmed baking sheet. Place beets in same bowl; toss to coat with any remaining oil in bowl and transfer to baking sheet. Sprinkle vegetables with salt and pepper. Brush onion slices with oil; sprinkle with salt and pepper. Grill vegetables until slightly charred and tender, about 12 minutes for beets, potatoes, and fennel, turning occasionally, and about 4 minutes per side for zucchini, peppers, onion slices, and mushrooms. Mound greens in center of 4 plates. Scatter onion slices over greens. Arrange vegetables around greens. Drizzle dressing over and serve.