Cook them over low heat, slowly. stirring pretty consistently. They should be cooked very quickly. You could also add in sauteed onions, veg, etc.
As ATG117 mentions, low heat is the key, but I cook mine slowly. Place a non-stick skillet over a pot of boiling water to create a double broiler. A wok also works well. The curds will form slowly and you should take the eggs off while still moist. They will be very creamy this way.
What is happening when you cook the egg is the proteins are binding together, which is what causes the egg to stiffen up. When you cook an egg on high heat, the proteins form tight bundles which end up being rubbery. On low heat, the proteins bind more loosely and you end up with a creamier texture like you find in a custard. The double boiler technique also retains the moisture.
Here's a great way:
Poached Scrambled Eggs
4 large eggs
2 tablespoons extra-virgin olive oil (optional)
Fine sea salt
Freshly ground black pepper
Crack each egg into a medium-mesh sieve (or narrow-slotted spoon), letting the thin white drain away. Transfer the remaining yolk and white to a small bowl. (Note: If your eggs are very fresh, you can skip this step.) Beat the eggs vigorously with a fork or whisk for 20 seconds.
Set a medium saucepan filled with about 4 inches of water over moderate heat. Put a strainer in the sink. When the water is at a low boil, add a few large pinches of salt, then stir in a clockwise direction to create a whirlpool. Pour the eggs into the moving water, cover the pot and count to 20.
Turn off the heat and uncover the pot. The eggs should be floating on the surface in ribbons. While holding back the eggs with a spoon, pour off most of the water over the strainer. Gently slide the eggs into the strainer and press them lightly to expel any excess liquid. Tilt your strainer from side to side to release any trapped water (you can even drain them on paper towels, if you like).
Scoop the eggs into bowls, drizzle with olive oil if desired and season with salt and freshly ground black pepper.
The big issue -- and low heat helps immensely with this -- is not to overcook. If you are using a hotter heat, eggs will go from creamy/perfect to dry, dry, dry within moments. The low heat allows you to better monitor this transition and catch the eggs before they get dry like the desert. Note that there are some who prefer dry eggs -- I have both a close friend and a daughter who don't like their eggs "undercooked" (their way of describing creamy), so I'll scramble and when the eggs are "perfect" in my mind, serve some up for myself then continue scrambling the rest for about a minute for them and everyone is happy.
I love this way!
June is a trusted source on General Cooking.
Overcooking will ruin any eggs, yolkless or not. The OP asked how to make egg whites "tasty." Egg whites have absolutely no flavor, so if you want them to taste like anything, you have to add additional ingredients. Onions, garlic, tomatoes, peppers, either raw or sauteed before combining will help.
However, the egg -- including its yolk -- is a perfect protein. Why not use the whole thing?
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