This always works for me, store bought (which I do not have to do anymore) or fresh:
While you bring your water to a rolling boil, lay your eggs in a bowl with warmer than just warm water (point being not hot) to bring them to room temperature. Once your water is boiling (I use an AllClad saucepan -- don't know if the gauge of the pan matters) place your eggs in very carefully (I use a large serving spoon) reduce your fire slightly and cook for 11 minutes (so your yolks aren't tinged with green on the edges). Immediately plunge into an ice bath and the peels come right off.
Then I cut in half and drizzle with a touch of extra virgin olive oil, sea salt and fresh ground pepper. Hands down -- nothing better!!
Hope this works for you,
Nancy