Fresh eggs get a bad rap when it comes to using them as hard boiled eggs. The reason is because the albumen, or the egg white, will stick to the shell of a fresh egg. Often you see advice to let the eggs age, because then it doesn’t stick as much to the shell. It is possible to use even an egg that has been laid the same day.
There seem to be many different ways of cooking (boiling) fresh eggs in their shell so that they peel. The method I use is as follows: bring the eggs up to room temperature. Bring your water to a slow boil, add salt, and ladle in the eggs. Cook at a slow boil for 15 minutes, then ladle out into a pan of cold water. Let sit in the water for awhile to cool, then the eggs can be stored in the fridge until you want to peel them. I use this method. It works and I am not going to fix it. I do need to use a timer or I over cook them every time.
Other methods I have seen but not used include adding a teaspoon of baking soda to the water, and using the traditional method of starting with cold water. Another idea that deserves merit is adding vinegar. I’ve also seen people suggest using olive oil. If your hard cooked eggs have a green tinge to the yolk, they are overcooked. Leave them in the hot water less the next time.
Another method is to use a push pin on the fat end of the egg. Slowly lower into soft boiling water. Soft boil for 15 minutes.