Place eggs in a saucepan large enough to accommodate the number of eggs you are boiling, in a single layer.
Cover eggs almost completely with COLD water. Cover saucepan and place on the stove over medium high-high heat (I use setting 8, where 10 is maximum).
When the water comes to a boil, reduce heat to low and set the timer for 9 minutes. Do not uncover the saucepan.
While you are waiting for the timer to go off, fill a large boil with ice water.
As soon as the timer goes off, drain the hot water from the pot and transfer the eggs to the ice water. If you are eating any of the eggs immediately, do so while still warm. Otherwise, keep the eggs in the ice water until completely cooled, changing water if needed. Refrigerate boiled eggs until ready to use.
To peel: Tap each egg gently on a flat service to crack. Firmly roll the egg back and forth in order to crack the egg all around. Gently peel the shell from the egg, rinsing the egg to remove any small shell particles as needed.
Notes
Boiled eggs are easiest to peel if you use eggs that are on the older side. If you see that your eggs are nearing or slightly past their best before date, they will be great to use for boiled eggs.