In a medium skillet heat the oil over medium-heat. Add the hash browns and cook for a few minutes until heated through, stirring occasionally. Stir in the zucchini and onions. Cover and cook over medium heat for 6 to 7 minutes, stirring occasionally.
In a medium bowl, whisk together the eggs, milk, salt and pepper. Pour the mixture evenly over the hash browns; using spatula, poke the hash browns in several places to help the mixture seep through to the hot skillet. Sprinkle the tomatoes on top. Sprinkle with salt and pepper.
Cover the skillet, and cook over medium-low heat for 6 to 7 minutes or until the eggs are just about set.
Sprinkle the cheese on top. Cover and cook for 2 to 3 minutes or until the cheese is melted.