Very similar to you! Also start with cold water, and bring to boil with the lid on. After it starts to boil, turn off the heat and let sit for 15 mins. It will be very easy to peel and no grey ring around the yolks. However, if I leave them in the cool all the way down, the green ring appears.
What is the purpose of the vinegar?
If I do soft boiled eggs, after the water starts to boil, I leave in for 2 mins and take out. Rinse them in cool water until they are handleable, then eat.
