In general, scrambled-egg pundits fall into two camps. Ignoring subtlety, I will dub these the European camp and the American camp. The European camp—exemplified by this delightful video of a chef with an outstanding French accent—holds that you should break eggs into a cold pan and scramble them over low heat (perhaps even over a double-boiler), stirring constantly. Taken to an extreme, European-style scrambled eggs are as smooth and silky as Ella Fitzgerald’s voice and are therefore, essentially, savory pudding. (Take note: Savory pudding is not necessarily a bad thing. After a long, hard day, savory pudding might be exactly what you want to eat for dinner. But savory pudding is not scrambled eggs.)
The American camp—so called because this is how you will find scrambled eggs cooked in most red-blooded American diners—maintains that eggs should be beaten thoroughly before added to a hot skillet, cooked over relatively high heat, and stirred relatively infrequently so as to allow large curds to form. At worst, American-style scrambled eggs have actually been allowed to brown in the skillet and resemble nothing so much as a very dry omelette torn to large shreds.
The right way to make scrambled eggs is a happy medium. (Call it the mid-Atlantic approach.) Everything about it is medium, in fact. You use a medium skillet. You cook the eggs over moderate heat. And rather than adding milk (too bland) or heavy cream (too rich), you add half-and-half (just right).