Place your eggs in a single layer at the bottom of a medium saucepan. Avoid overcrowding the pot; if necessary, use a second pot.
Cover the eggs with cold water by about an inch. This ensures even cooking and prevents cracking.
Place the saucepan over high heat and bring the water to a rolling boil.
Once the water reaches a full boil, immediately turn off the heat, cover the saucepan with a lid, and let the eggs sit in the hot water for 10-12 minutes. The exact time will depend on the size of your eggs and your desired level of doneness. 10 minutes for firm yolks, 12 for very firm.
While the eggs are steeping, prepare an ice bath. Fill a large bowl with cold water and plenty of ice cubes. This rapid cooling stops the cooking process and helps with peeling.
Using a slotted spoon, carefully transfer the cooked eggs from the hot water into the prepared ice bath. Let them cool completely in the ice water for at least 10-15 minutes.
Once cooled, gently tap each egg on a hard surface to crack the shell all over. Start peeling from the larger end of the egg, where there's usually an air pocket. The cold shock should make the shell and membrane separate easily.