Boil milk in a small saucepan. Add salt and oats. Cook for 5 minutes over medium heat stirring occasionally. Transfer oatmeal to a medium bowl and allow it to cool.
Crack eggs into bowl with oatmeal. Add ground pepper. Whisk eggs and oatmeal until combined.
Heat vegetable oil in an 8 inch non-stick fry pan. Pan fry tomatoes for about 30 seconds on each side. Remove tomatoes from fry pan.
Pour eggs and oatmeal mixture into fry pan. Sprinkle green onions on the top. Let the eggs cook and set over medium heat, about 2 minutes.
Flip the omelet and arrange pan fried tomatoes onto one half of the omelet. After 1 minute, fold the other half of the omelet over the tomatoes.