Crack the eggs open into a mixing bowl. Season with salt and pepper then whisk together. Stir in the basil.
Halve the tomatoes and slice up the cheese. Heat the olive oil in a large frying pan over medium-high heat. Fry up the tomatoes until they start to soften.
Pour the eggs on top of the tomatoes. Once the eggs start to set on the bottom, add the mozzarella cheese.
Lower the heat to medium-low and allow the omelet to fully cook through. Remove from pan and serve.