I asked if the youngling might mean hard boiled eggs. Turns out that was what she wanted.
Well, I made "eggs with a ball in the middle" this evening, and was quite pleased with the result. Om, nom, nom.
I haven't made them in ages. (Decades?) so I turned to the internet. Yup, pages of recipes for making hard cooked eggs; turns out you don't really boil them much at all, just get the water going, and then let the heat energy applied to the water do the cooking.
Here is a link to the recipe I used, if you want it. http://www.incredibleegg.org/recipe/easy-h
They suggest using 7 to 10 day old eggs to make peeling the shells off easier, but my eggs are often all eaten before then. I left this dozen on the counter at room temperature for about 24 hours before cooking them. First two peeled easy peasy. The rest are in the fridge for later. Will let you know if they all peel this well.