Heat 1 inch of water in a steamer.
Place cauliflower, green peppers, and carrots in a steamer basket or colander, cover, and steam for 4 minutes.
Place steamed vegetables in a glass bowl and toss with mushrooms.
Heat tomato juice and cornstarch in a saucepan over low heat, stirring until juice thickens.
Combine tomato juice with balsamic vinegar, red wine vinegar, onion, oregano, and parsley.
Pour dressing over vegetables and chill, covered, for 3 hours.