Preheat grill to high. Whisk eggs, eggwhites and 1 tablespoon water in a bowl, until just combined. Season with pepper.
Heat 1/2 teaspoon of oil in a small, non-stick frying pan on medium. Pour in 1/4 of egg mixture. As egg begins to set, arrange slices of tomato and shallots over omelette. Cook for 2 minutes.
Place frying pan under a preheated grill to finish cooking eggs. Slide onto a serving plate and cover with foil. Repeat with remaining mixture and ingredients to make 3 more omelettes. To serve, slide omelettes onto warm plates and top with a few basil leaves and a drizzle of pesto. Serve immediately.