Put the eggs & spinach into a blender and process until smooth. Add the pesto and combine.
Lightly grease a pancake or flat frying pan and pour in half of the mixture, letting it spread out evenly.
When the omelette is almost cooked through place 4-5 pieces of tomato slices in the middle section of the omelette. Scatter half of the cheese all over and cook for another minute or so, until the surface has completely set.
Scatter some basil leaves over the tomatoes and season with ground pepper. Double fold the omelette over the tomato section, creating an envelope shape (like you do with crepe) and cook for a few seconds.
Slide the omelette to a plate and make another one, repeating the above with the remaining egg mixture.
Serve warm.