This is the ultimate breakfast egg for small children. They just love dipping in the toast and scooping the rest out with a teaspoon. It must be a soft-boiled egg with the top chopped off.

picture from the Eat Live Run blog
The physics and chemistry of cooking an egg is all about cooking the white and the yolk, at 80 degrees and 70 degrees respectively.
And knowing they cook from the outside. And that eggs may continue to set after they are turned off, unless put in cold water to stop the cooking.

Because of many variables you will have to experiment with your own eggs in your own kitchen. The variables are:
• egg temperature at start
• size of egg
• freshness of the egg
• temperature of water at start
• the base thickness and type of metal of the saucepan
• ratio of water to egg (one egg in a big saucepan will boil slower, and therefor cook for longer up to boiling, than in a small pan)
• Boiling Point is not exactly 100 degrees C, as this changes down with altitude and lowering barometric pressure and up with a solution like salt in the water
• The time taken to get water to boiling depends on heating method; induction, gas and electric coil are all different, the longer it takes to get from 70 to 100 degrees the less time will be needed after the saucepan boils.

Cooling down time depends on
• thickness and type of metal saucepan
• if the saucepan is left on the hot plate
• the room temperature
• how much water per egg you have (greater mass cools slower and cooks more)

The solution is to reduce the variables so the times and results become standard.
1. Take all eggs the same age and size from the fridge, which has a constant temperature
2. Use a heavy base stainless steel saucepan
3. Reasonably tightly pack the eggs, so with one or two eggs use a small saucepan
4. Cover eggs by 20mm with cold tap water
5. Cook on high until boiling
6. Then EITHER
keep boiling for around 3 minutes and then remove with slotted spoon, cool with cold water to stop the setting process AND SERVE

Remove from heat when boiling (by shifting off electric coil and plate)
Leave to keep cooking in water for three, four or five minutes depending on size and starting temperatures AND SERVE

Serve in an eggcup with teaspoon and the top cut off and with buttered sticks of toast soldiers, salt and place parsley sprigs on the side.