Bring water and oil to a gentle boil in a pot large enough to lay the eggs in one layer.
Add the eggs one at a time gently to the boiling water using a spoon.
Boil for exactly 13 minutes for hard boiled eggs, or 10 for medium, and 3-6 for soft (depending on how runny you want the yolk.
Meanwhile, prepare an ice bath with about a tray's worth of ice and enough water to completely submerge the eggs.
Remove the eggs with a slotted spoon and place immediately in ice bath.
Allow to sit for at least 10 minutes in bath.
Peel gently, preferably under running cold running water.
I used large eggs for this. If you use smaller eggs, you may need to cook for less time.
Nutrition information is for one egg with no oil, since most of the oil stays in the water.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.