Why is energy conservation suddenly coming up and what does it have to do with time dilation? All you really need to know is what Geezer was saying--that if you put your timer and egg next to each other, then they should both agree on what three minutes is.

The reason i brought energy conservation up was that to time and cook the egg you need a set amount of energy in a set amount of time

And a joule is a unit of energy in the International System of Units, It measures heat, electricity and mechanical work.

The joule is a derived unit equivalent to a newton-meter, or a kilogram-meter squared per second per second.

A joule is also:

A unit of electrical energy equal to the work done when a current of one ampere is passed through a resistance of one ohm for a period of time of one second.

A unit of energy equal to the work done when a force of one newton* acts through a distance of one meter.

In the meter-kilogram-second (MKS) system, a newton is the unit of force required to accelerate a mass of one kilogram one meter per second per second,

So you will notice time is a factor in the measurement of the work heat equivalence and as we have already noted earlier in this post at the center where in GR time is slower will the energy interactions there not disagree with the International System of Units as regards the laws thermodynamics.

similar to the fact that a particle at the centre of the earth would seem to travel faster than one at the surface according to G R, so distance travelled would disagree with the International System of Units.

But, what exactly is this 'energy' we're speaking of, is it the same type we find in our combustible engine? and furthermore, if there exist this kind of phenomena, why couldn't we speak about gravity as a 'force'?

Energy is Energy it just takes different forms and yes even in GR they must be trying to detect a variation in gravity as some kind of force or maybe they will detect a variation in the gravitational force.