In a small bowl, whisk the eggs with the egg white and set aside.
Coat small nonstick skillet with 1/2 teaspoon of the oil and heat over medium heat. Cook the tomato, onion, and pepper for 4 to 5 minutes, or until tender. Transfer to a bowl.
Wipe the skillet and then coat it with the remaining 1/2 teaspoon oil. Set over medium-high heat. Add the reserved eggs and cook for 2 minutes, lifting the edges of the omelet as it sets and allowing the uncooked egg to flow to the edges of the skillet.
Add eggs to skillet, and cook for 2 minutes, lifting edges with spatula to allow uncooked egg mixture to flow to the edges and cook.
As center of omelet begins to set, spoon the cooked vegetables on one side of the omelet and top with the spinach. Season with the salt. Gently fold 1 side of the omelet over the other. Cook for 1 minute to let the omelet set. Slide the omelet from the skillet to a plate and serve with 1 slice of melon.