Bring a pot of water to a simmer. Choose a pot that allows all eggs to sit on the base of the pan without stacking, and use enough water so that the eggs will be covered by at least 1 inch of water.
Meanwhile, place the eggs you’d like to cook in a bowl of warm water for 10 minutes. (This will temper the eggs, preventing the eggs from cracking when they’re lowered into the simmering water.)
When the pot is simmering, gently transfer the eggs from warm water to the simmering water one at a time with a slotted spoon. Maintain a gentle simmer (not a boil), adjusting heat as needed, and cook the eggs 6.5-7 minutes. (I recommend using a timer!)
While the eggs cook, fill a bowl with cold water and a few pieces of ice. After 6.5-7 minutes, use the slotted spoon to transfer the eggs from the pot to the bowl of ice water. Allow to sit a few minutes, until cool enough to handle.
Then, gently tap/crack each egg all over, beginning with the air pocket (the wider end of the egg), and return to the ice water to sit for 10 minutes. (This will separate the membrane from the egg, allowing the shell to peel away easily.)
Peel the eggs one at a time in the water. Enjoy right away or refrigerate up to two days!