Combine the eggs, salt, and milk in a medium bowl and whisk until the mixture is homogeneous and frothy, about 1 minute. Let rest at room temperature for at least 15 minutes. The eggs may darken in color significantly. [Editor's Note: On some rushed mornings and evenings, we confess to having blatantly ignored this direction to wait 15 minutes. And to be honest, the eggs still turned out terrific.]
Melt the butter in a 10-inch nonstick skillet, carbon-steel skillet, or cast-iron skillet over medium-high heat, swirling the pan as it melts to coat it evenly.
Add the egg mixture to the pan and wait, without touching the eggs, until the eggs seem to have firmed a little at the edges and on the bottom. You may need to reduce the heat to medium so as to prevent any browning. Scrape the pan with a silicone spatula as the eggs solidify. Then continue to cook, scraping and folding constantly, until the eggs have formed solid, moist curds and no liquid egg remains, about 2 minutes. The eggs should still appear slightly underdone but don’t worry, the residual heat will continue to cook the eggs even after you remove them from the heat and onto a plate. Serve immediately.
Notes
Cooking For Two Variation
Follow the instructions exactly as above except use half the ingredients and a 6- to 7-inch skillet.