I used to start a thread every spring on this but got tired of people unwilling to try my method criticizing it and telling their methods such as baking, pressure cooker, just buying a gadget to bake or microwave them in the shape of a boiled egg. I tried multiple suggestions on here, vinegar, salt, aging the eggs with variable results. Finally I tried the method I found on here that was totally against every cookbook I have ever seen.
For me the age of the egg makes no difference. I have used 3 week old eggs from counter, 1month + from fridge (set on the counter awhile to warm up) and eggs fresh from the nest. It works at least 90% of the time for me.
Bring a pan of water to a boil. You need enough water so the eggs will be covered. When it is reaches a rolling boil carefully add eggs (I use a spoon to lower them). Cover, Return to a boil if needed. Then turn off heat but leave on the burner for 11 to 15 minutes for hard boiled eggs. Dump water, flush with cold water, add some ice, crack slightly and let set in cold water until cool enough to peel. It works best if you start at the large end to peel them and if you peel them right away. I have less success with perfect eggs when I refrigerate to peel later.,
I hope this works for you.