Ah, the mystery of egg-making! We all want that perfectly cooked egg. Whether hard, medium, or soft-boiled, the mighty egg has tripped up many chefs and created a plethora of techniques. Here's how my Mama taught me. One thing to note: start your eggs out at room temperature regardless of what you're making.
Soft Boiled
Mama didn't make these for us as children because to most kids a runny yolk is "blech!" But she did make them when I got older and taught me to do them as well. The thing that trips most people up is how to use a soft-boiled egg. Today they're served on avocado toast or in a breakfast bowl. But both soft and medium-prepared eggs used to be served in "egg cups". These are now collectibles if they're at least "vintage". You placed the finished egg, in its shell, in the cup and then lightly knifed around the top (about 1/2 inch from the top) to reveal the inside and scooped it out to eat. Served with toast, possibly meat, or some fruit.
The soft-boiled method results in a gelatinous white and runny yolk with no solid. Yes, the white holds but it holds like Jell-O. So you're not talking about the classic firm white. There may be some loose white towards the yolk which is why many used to break in and scoop it to toast.
Bring water to the boil (I recommend brown eggs for this); make sure the water covers the eggs.
Cook for 6 minutes from the time of boiling.
Put in your egg cup and crack the narrow end and cut out.
This is for LARGE eggs only.
Jammy Eggs (medium boiled)
In a large enough pot to cook the number of eggs you'll need, put in enough water to cover the eggs by 1-2".
Bring to a boil.
Add in eggs slowly, one at a time.
Time for eight minutes exactly.
Remove and place in an ice water bath for 15 minutes to stop the cooking.
Place in an egg cup and tap around the top (pointed top) to open.
These are perfect for Ramen!
Traditional Hard Boiled
The biggest problem here is over-boiling. Then you get the yucky green color around the yolk and a potentially very dry or rubbery yolk. So here's how to stop that.
Place in a pot of COLD water and cover with the water by 1"-2".
Place on high to boil and boil to eight minutes.
Remove the pan from the burner and allow to sit another 8 minutes in the pot.
Run under cold water until cool and place in fridge.