My hard-boiled eggs come out perfectly 99% of the time with no grey ring and not overcooked in the least. I wish someone had told me sooner the trick to making them this way:
The first trick is to make sure your fingers are wet when you lift the eggs from the carton. Having wet hands actually makes for a better grip on the eggs (you would think the opposite, huh?). Put them in a saucepan where they have plenty of room. Fill the pan to cover the eggs by at least 1/2 inch.
Bring the cold water and eggs to a rolling boil. Quickly cover with a lid and TURN THE STOVE OFF (or remove from heat if you have an electric range). Set your timer for 13 minutes (don’t lift the lid!). When the timer goes off, immediately put the eggs into an ice-water bath to quickly cool them down. This is what I was told prevents the grey ring.
Then, to peel, start at the fatter end of the egg. A little air pocket exists under there that will make it easy to slip your spoon in (upside down) and help force the egg from the shell. Again, you would think the opposite but nope, the pointy end does not house an air pocket.
Be sure to rinse the egg and pat dry before setting aside in the bowl. If you by accident mix up your fresh eggs with your hard-boiled eggs, you can spin the egg like a top. If it spins, it’s hard-boiled. If it immediately lays down and won’t spin, it’s raw.
To make egg salad, I find it easier to press the egg through one of those wire slicers that slices them in even segments. For 6 eggs, I put about 2 heaping Tbsp of mayonaise (you can always add more to taste but it’s impossible to take away excess mayo), a tsp of regular yellow mustard, salt and pepper (come people use white ground pepper but I’m old-fashioned). No fancy spices, just the basics.
I like to make an egg salad sandwich with sweet, dark brown squaw bread and a slice of lettuce. Oh, it is soooo good! Try it and let me know how it worked out for you!