The steaming time will vary depending on the size of your eggs, how cold your eggs are to begin with, the altitude of your location, how vigorous the water is boiling, if your eggs are in a single layer or are stacked, and how soft or firm you like your hard cooked eggs. So you may need to experiment to find the right timing for your situation.
A steamer basket is convenient, but not necessary.
1 Prepare pot and steamer basket: If you are using a steamer basket, fill a saucepan with as much water as needed to reach the bottom of the steamer basket (about 1 inch or so).
If you are not using a steamer basket, just fill the bottom of a saucepan with 1/2 inch of water.
2 Heat water to boiling, add eggs to pot: Heat the water on high heat until it is boiling and producing steam.
Turn off the heat and gently place the eggs at the bottom of the steamer basket or the bottom of the pan.
Turn the heat back on again to medium high, and cover the pot.
This method works best if the eggs are in a single layer, but you can double them up as well, you'll just need to add more time to the steaming time.
3 Set your timer and steam the eggs: Set your timer for 6 minutes for soft boiled, 10 minutes for hard boiled with a still translucent and bright yolk, or 12-15 minutes for cooked-through hard boiled.
If you have doubled up the eggs in the pan and they are not in a single layer, you may need to add a couple minutes or so to the cooking time for hard boiled.
The size large eggs used in these photos were cooked to my satisfaction after 15 minutes when I cooked 6 in a single layer, and 17 minutes when I cooked 12 in the pan.
Note that many things will influence the steaming time, including altitude and the size of the particular eggs you are using. I recommend removing one egg a couple minutes before you think it should be done, rinsing it with cold water, and breaking it open to see if it is done enough for you.
4 Remove eggs to a bowl of icy cold water: Remove eggs with a spoon to a bowl of cold water or ice water, or run cold water directly into the pan to cover the eggs and quickly cool them down.