@dave
Wait, what?
Why wouldn't you be able to melt an egg? It is made of the same materials as anything else.
Hafnium carbonitride (HfCN) is a refractory compound with the highest known melting point of any substance to date and the only one confirmed to have a melting point above 4,273 K (4,000 °C; 7,232 °F) at ambient pressure.
So, at 4 000 °C, There should not be a single element or compound inside of an egg left solid.