I prefer this method:
Place eggs in pot with cold water. Bring to boil. As soon as water is boiling, cover the pot, and turn off the stove top. Leave eggs in pot, with the stove off, for 15 minutes. Pour out the hot water and put the eggs in an ice bath for a few minutes. Peel. Done.
I think continuously boiling eggs often overcooks them. This method creates perfectly cooked hard boiled eggs.
I'm going to have to figure out how to improve my hard boiled egg routine. I've been eating them at the hospital cafeteria because I can't figure out what the runny, scrambled yellow stuff actually is. At least the hard boiled ones are eggs...right? The basic method is this: put eggs into a vigorously boiling large pot, forget about them while you're preparing the weird scrambled powder. Serve them before they burst open from boiling too long, mix in all the broken ones from yesterday no one wanted, or maybe make a quiche out of those to serve on Wednesdays.
Add a bunch of salt to the water. More salt than you're comfortable with. Boil for 10-12 minutes or so. Immediately to an ice bath (just running cold water will work too).
If the shells don't crack and peel I like to take the egg, (gently) smack it on the table and roll it with my palm. Should create a nice little "fault line" around the center, then the halves just pull off.
Something we used to do in a restaurant kitchen when needing to peel a boat load of hard boiled eggs.
Kitchen hack: Take a hard boiled egg and place it in a straight walled drinking glass. Fill with water to just over the top of the egg. Put your hand over the top of the glass and shake the glass with egg and water vigorously up and down for about 15-20 seconds. Pull out the egg, and the shell will slip right off.
Physics: As the egg is shaken in the glass, hydraulic pressure from the impact pushes water in between the broken shell and the egg. Results: the shell slides right off.
Need to make a lot of eggs? Bake them:
Set the oven to 320 degrees F and bake for 30 minutes. When the eggs are done fill a large bowl with ice water and move the eggs into a bowl. Peel the eggs as soon as they are cool enough to handle, then return them to the ice bath to thoroughly chill.
On a side note, I thought I had read that more recently the understanding is that blood cholesterol is not so impacted by the diet's intake of cholesterol, but more so by hydrogenated oils. Even bad enough that they may be banned?
I started steaming mine after frustration with tough-to-peel eggs. This has worked well:
1. (for a dozen) boil a few inches of water in a 6-8 quart pot
2. When boiling fully, add cold (room temp or fridge temp) eggs to a steamer basket
3. lower steamer basket to somewhere above the water, and cover the pot.
4. Steam over moderate-high heat for 15 minutes (this makes the yolk hard-boiled, less time for soft-boiled).
5. Rapidly cool eggs in cold water bath immediately after removing from heat.
6. Peel using your favorite method. I like the cover and shake in a glass bowl method.
I think the key is the placing of cold eggs in already-boiling water (or steam, in my case). I'm told this is the factor which makes peeling easy (as opposed to gradually heating eggs and water).
I haven't gone a single day in the last two years without eating at least three eggs. Usually around 6 a day, and sometimes as many as a dozen. Nothing horrible has happened.
I've naturally avoided mentioning this to my doctor, although I did get a battery of tests done when she found out I drink protein shakes. I don't recall the numbers but my cholesterol was normal, no red flags. Eggs rule. Especially when scrambled with breakfast sausage, or fried in bacon grease.