Cover the pot and let the eggs sit in the hot water. If you prefer them with their yolk soft, keep them for 9 minutes. If firm eggs are your preferred choice, let them in the pot for 11 to 12 minutes.
Once you take them out of the pot of hot water, place them into an ice-cold water for around five minutes.
And yes, for smoother peeling, crack and peel them under running water.

If you want to prevent cracking while boiling them, add a tablespoon of vinegar or a pinch of salt in the water.
Boiled unpeeled eggs are safe to eat in a week time, while the peeled ones can be stored for 2 to 3 days before consuming.