First, allow the eggs to come to room temperature, or put them in a bowl of warm water for a few minutes to take the chill off. This will prevent them from cracking when they are added to boiling water.
Choose a pan wide enough to hold all the eggs in one layer, and fill it with just enough water that will cover the eggs (do not add the eggs yet). Fill a bowl with ice water and set it near the stove.
Place the pan over high heat and bring the water to a boil. Use a large spoon to gently ease the eggs into the water a few at a time. Once the eggs are all in, start timing for 3 1/2 minutes. When the time is up, scoop the eggs into the ice water and allow them to chill for about 5 minutes.
The easiest way to peel the eggs is to put a few at a time, with a little water, into a glass jar with a lid. Shake the jar vigorously a few times to crack the shells. Peel the eggs under cold running water, using a small pointed knife if necessary to help get under sticky edges. The peeled eggs can be put into a small bowl and covered and refrigerated for up to a couple of days.