About 1 hour before serving or day ahead: In large Dutch oven or Wok over medium-high heat, in 2 tablespoons hot salad oil, cook carrots and 1/4 teaspoon salt until carrots are tender-crisp, about 3 to 5 minutes, stirring often. With slotted spoon, remove carrots to large bowl. In 1 more tablespoon of hot oil, cook pea pods and 1/4 teaspoon salt 1 or 2 minutes, stirring. Remove to bowl.
In 3 more tablespoons hot oil, stir mushrooms and 1/4 teaspoon salt until mushrooms are coated. Cover; cook 3 to 5 minutes, stirring occasionally. Remove to bowl. In 1 more tablespoon hot oil, cook tomatoes until heated through, about 1 minute, stirring. Remove to bowl. In 2 more tablespoons hot oil, stir broccoli, cauliflower, and onion until well coated; add water and 1/2 teaspoon salt. Cover and cook 5 to 10 minutes until tender-crisp, stirring occasionally.
Remove Dutch oven or Wok from heat. Return all vegetables to Dutch oven or Wok; add soy sauce; mix well. Spoon vegetables onto large platter. Serve hot or refrigerate to serve cold later. Makes 10 servings.