Beat the eggs with the salt until the whites and the yolks are completely combined, with no spots of egg white remaining.
Over medium-low heat, melt the butter in a skillet, then pour in the eggs.
Using a rubber spatula, constantly scrape the bottom of the pan while shaking the pan in a circular motion to ensure that the eggs cook slowly, forming only small curds, about 1-2 minutes.
Once you start to see the bottom of the pan for more than a second after scraping, push the eggs into a round circular shape. Cook until the edges solidify, then tilt the pan and carefully roll the omelette on itself.