I've heard of the "steaming" method (putting eggs in cold water then bringing to a boil and removing from heat) but I've never tried it.
I've always had success with bringing the water up to a full boil, then gently/slowly putting in the room-temp eggs (I use tongs) and boiling for 13 minutes.
Once done, rinse under very cold water: dump the boiling water, fill the pot with cold water, dump the water, fill the pot with cold water, dump the water, etc. until the eggs are cool to the touch . . . all the while shaking the pan in order to crack the eggs.
Even with eggs that I store for later in the week, I'll still peel them and store them in a closed container.