<<Disclaimer: Verify this information before applying it to your situation.>>

Someone asked a very good question.

If you remove the 'uncooked' middle are the eggs cooked?

Yes, they are well cooked as they are in the oven over half an hour at high
heat.  The part you remove is the softer middle which is really cooked, so
that you have the shell left to stuff.

Sorry for the poor choice of words - it is what the recipe says.

Jessie