What's the right way to hard boil eggs?
I've never adjusted the length of time based on number of eggs. As long as the water is boiling I don't think it would take any longer to cook a dozen than to cook one (it might take the water longer to come up to boiling, I guess).

For hard boiled I normally bring them up to the boil and then turn the heat off, and leave them for 15 minutes. If you like them less well-cooked, you could reduce this to 12 minutes. Then empty the pan and re-fill it cold water a couple of times to cool them down quickly. Leave rest of them sitting in the cold water while you prepare each one.