Warm oil in a heavy large nonstick skillet over medium-high heat. Sauté asparagus, zucchini, mushrooms and sliced green onions until golden brown. Add tomatoes to warm through and sprinkle with ½ teaspoon salt.
In a medium bowl, whisk eggs, grated Parmesan cheese, 1/2 teaspoon salt and 1/4 teaspoon pepper to blend well.
Reduce heat to medium. Spread vegetable mixture in single layer in skillet. Pour egg mixture over vegetables. Cook until eggs are very softly set, tilting skillet, gently running rubber spatula around edges and allowing uncooked egg portion to flow underneath, about 4 minutes. Add cheese before tilting skillet and folding omelet in half. Slide omelet out onto plate, cut omelet into wedges and serve.
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A way to involve kids into healthy eating is allowing them in the kitchen and let them cook, this is what this video conveys. The little chefs in the video make an omelet with vegetables for a quick breakfast.