Add eggs and salt into a medium bowl. Using an immersion blender or whisk, whip eggs until completely homogenous and pale yellow in color, about 30 seconds. Add salt.
Melt butter in an 8" nonstick skillet over medium-low heat. Let it cook until foam subsides then add the eggs to pan and let cook undisturbed. Cook until a thin layer of cooked egg appears around the edge of the skillet.
Sprinkle Parmesan cheese in an even layer over eggs, then using a rubber spatula, push eggs all the way around the circumference of the pan, then across the bottom. Continue to push eggs around and across pan until fluffy about 2 minutes.* They will be barely set and will still look runny on top. Let cook for another minute or two until they are set to your liking, then immediately serve and sprinkle with minced fresh basil.
*Cook to your liking. Super soft scrambled are still runny