Mom's Favorite Cheesy Scrambled Eggs

Steps

1. 1Crack all 4 eggs directly into medium mixing bowl, then add half and half and 1 pinch salt. Whisk vigorously until mixture is pale, foamy, and uniform in color, with no streaks of yolks or egg whites. Let egg mixture sit 5 to 15 minutes, to allow salt to be fully absorbed.
2. 2Heat skillet over medium heat. When pan is hot, add butter to skillet and heat until butter has melted completely and begins to foam.
3. 3Swirl skillet to fully coat bottom with butter, then pour egg mixture directly into center of skillet. Immediately reduce heat to medium-low.
4. 4Let eggs cook, undisturbed, until edges barely begin to set. Using a spatula, in wide strokes, gently fold eggs into themselves repeatedly, until approximately half of eggs have set.
5. 5Remove skillet from heat, then add pieces of American cheese to eggs. Continue gently folding eggs until cheese has melted and incorporated into eggs. Eggs should be fully cooked, but not dry, matte, or overly solid. Ideally they should stay fluid and look glossy, but not be runny or undercooked. Note: this is how I prefer my eggs; they're incredibly creamy. If needed, continue cooking until desired doneness is achieved.
6. 6Transfer cooked eggs to plate(s) and serve immediately.