Place one tablespoon of the butter in a small bowl along with the cream cheese and one tablespoon of basil. Microwave for about 30 seconds to melt then stir together to combine fully. Stir in the mozzarella and set aside to cool slightly.
In a separate small bowl, whisk the eggs along with the salt and pepper. Whisk in the basil butter mix.
Place the remaining tablespoon of butter in a medium sized pan and heat over medium heat.
Pour the egg mix into the pan and cook, stirring constantly to scramble the eggs.
Once the eggs are cooked to your liking, divide between two plates and top each plate with the remaining basil. Enjoy while hot.