You can get moist, creamy scrambled eggs without using milk! In French, eggs cooked just barely to having set, but which are still moist, are called "baveuse" or runny/dribbly. Literally, though, "baver" means "to drool/slobber". On top of that, I think scrambled eggs cooked in such a manner are drool-worthy.
This was a miraculous discovery to me, as I've long thought that beating in milk with the eggs was necessary. However, I tried just beating in a tablespoon of water per egg (and a pinch of salt), which helps to give the eggs some volume and lightness, and the rest is up to technique (from The New Best Recipe). Of course, if you can have milk and butter, it tastes even better.
You can either use a fork and slowly stir the eggs in a wide circular motion, with the fork tines held horizontally--parallel to the plane of the skillet, or use a spatula and gently push the eggs from one side of the skillet to the other. As the curds form, you start to gather them up into a mound. Remove from heat as soon as the eggs are just set and still wet-looking, and serve immediately. The New Best Recipe says to use high heat, but I've found that I need to use lower heat on my stove for the rate of cooking that they describe in their recipes.
I beat in chopped scallions with my egg this time.
On another somewhat related note, good timing is also key to getting your omelette eggs to be similarly soft and moist. Though with omelettes, you don't need water or milk mixed in with the eggs (thanks again to The New Best Recipe). Once the egg is just set and the top still moist (baveuse), remove the skillet from heat before proceeding with the filling and folding. If you just turn off the stove, but don't move the skillet, the residual heat will keep cooking the egg more than if you move the skillet away.
The filling is leftover black bean and corn salad I made. Gotta remember to add salsa...
Hmm, I'm not getting the "lovely brown exterior" described in the book, though. The moistness of the eggs are just right, though. I think I need a smaller skillet, so that the bottom can brown before the top cooks through and dries out, since the egg layer won't be spread out as much. I'm using a 10", so go for smaller than that for a 2 egg omelette. The New Best Recipe says 9" for the 2 egg omelette; 8" for a 2 egg scrambled egg, but I haven't had a problem with a 10" for a 2 egg scrambled egg.