Break the eggs into a bowl and whisk well with a fork. Season, then add 2 tablespoons of water and the chopped basil. Mix again.
Heat the olive oil in a large frying pan / skillet. Gently fry the sliced red onions for a couple of minutes until soft. Pour in the egg mixture and cook over medium meat for around 3-4 minutes, drawing the mixture from the sides to the centre until the omelette is half cooked.
Add the small cherry tomatoes to the omelette (cut-side up), and the crumbled feta cheese and cook for a further 2 minutes. Slide onto a warmed plate and serve immediately.