Whisk the eggs in a mixing bowl until well combined.
Season with salt, pepper, and optional heavy cream.
Heat a non-stick omelette pan over medium heat.
Melt the butter or warm olive oil in the pan.
Pour in the egg mixture, letting it spread evenly.
Use a spatula to gently pull the edges toward the center as the eggs set.
Spread basil pesto evenly over the omelette.
Sprinkle mozzarella and optional parmesan or tomatoes on top.
Fold the omelette in half and cook briefly until cheese melts.
Garnish with fresh basil leaves and red pepper flakes before serving.