1. Preheat oven to 350°F. In large bowl, with mixer at high speed, beat egg whites until stiff peaks form. In small bowl, with same beaters and with mixer at high speed, beat egg yolks, 2 tablespoons water, and 1/4 teaspoon salt until very thick. Fold egg-yolk mixture into beaten egg whites.
2. In 10-inch oven-safe skillet over medium-low heat, in 1 tablespoon hot salad oil, cook egg mixture about 3 minutes or until top is puffy and bottom is golden when gently lifted with a pancake turner.
3. Place skillet in oven. Bake about 10 minutes or until top of omelet is golden and springs back when lightly touched with finger.
4. Meanwhile, in 3-quart saucepan over medium-high heat, in 1 tablespoon hot salad oil, cook radishes, mushrooms, zucchini, onion, savory, and 1/4 teaspoon salt, stirring frequently, until vegetables are tender-crisp. Add tomatoes with their liquid. In cup, stir cornstarch and 2 teaspoons water until smooth; stir into vegetable mixture. Cook, stirring, until mixture thickens slightly. Remove from heat.
5. Loosen side and bottom of omelet from skillet; sprinkle cheese over omelet. Spoon half of vegetable mixture over half of omelet; fold omelet over vegetables. Tip skillet; slide omelet onto warm platter. Spoon remaining vegetables around omelet.