Heat a non stick pan or skillet and crack the eggs to the hot pan (you may crack the eggs to a bowl and then add to the hot pan if that is easy for you).
Also add the butter or oil, as needed to fry the eggs.
As the egg whites begin to set (about 1 to 2 minutes), close the pan with a lid.
You may also sprinkle a little water (about 1 tablespoon) for even better steaming of eggs but make sure to immediately close the pan with lid once the water is sprinkle, or it may splatter.
Once the pan is closed with lid, reduce the heat to low and cook for another 1 to 2 minutes until a white films form over egg yolks.
If you want the egg yolks to be runny like in over easy eggs, you can stop the cooking, open the lid and carefully transfer the basted eggs to a serving plate using a good spatula.
If you want only slightly runny yolks like in over medium eggs, wait for another 1 more minute and then stop the cooking and transfer the eggs from the hot pan so the egg yolks will not be too runny, but it will be soft and have a texture of jelly.
If you prefer completely cooked egg yolks like in over hard eggs or over well eggs (as I have done here), continue cooking for another 2 to 3 minutes in low heat until the yolks are completely cooked and set and the yolks resemble that of boiled egg yolks. That way, the yolks won't be runny at all.
It is your personal preference how long you want to cook the basted eggs, once the white film has formed over the yolks.
You do not need to flip the basted eggs as they are done without flipping itself.
However, you may flip and cook the other side too, if you wish.
I prefer not to flip the basted eggs, because they are just perfect without flipping and soft and delicious.
Once the basted eggs are done to your liking, immediately and carefully transfer the eggs to a serving dish, season with more salt and pepper if you wish, enjoy the eggs while it is still hot or warm for the best results!