In a large nonstick pan with sloped sides (even a wok shape works), melt the butter over medium-low heat, being careful to not brown the butter. If it begins to bubble, the heat is too high, so lower the heat to cook the eggs properly. (Slow and low like BBQ is the way to go with eggs.)
Meanwhile, in a large bowl, add the eggs and 1 teaspoon cold water. Vigorously whisk until frothy and smooth. Swirl the pan around to coat the butter on the bottom and up the sides. Pour the eggs into the pan and let sit for a few seconds. When the eggs begin to lightly set on the bottom, use the whisk to gently beat the eggs, then allow them to sit for just a few seconds between beating them again. Curds will begin to form and increase throughout the cooking time. Repeat this process of whisking then resting the eggs for a few seconds until about 50 percent of the eggs are set and the rest are still wet. At this point, sprinkle the eggs with a pinch of salt and pepper and continue to whisk and rest alternately. Once the eggs are 75 percent done, add the cheese and from this moment, continue to whisk the eggs until done. This entire process from pouring in the eggs to them being finished should take 8 to 12 minutes; this isn't a race, only a journey to the best scrambled eggs ever. Remove from the heat and continue to scramble in the last seconds. Serve warm.
While scrambling, if a thin film of egg begins to set on the edges of the pan while you are whisking away, the heat is too high and you are whisking a bit too fast. Be gentle and take your time. If this happens, very quickly before it browns, incorporate those dry edges back into the eggs with a twist of the whisk and they'll disappear.