Preheat oven to 400°F. Combine first 6 ingredients in heavy large skillet. Bring to simmer. Reduce heat to medium-low, cover and cook 10 minutes, turning vegetables occasionally.
Using slotted spoon, transfer half of vegetables to 9x13-inch baking dish. Season with salt and pepper. Sprinkle 3/4 cup cheese over. Top with remaining vegetables. Pour cooking liquid over. Season with salt and pepper. Sprinkle 3/4 cup cheese over. Cover with foil; bake 45 minutes. Uncover; sprinkle with remaining 1/2 cup cheese. Bake until liquid is almost absorbed, about 55 minutes. Cool 20 minutes before serving.
