I know that 玉子 is read "tamago". I also know that 醤油 is read "shouyu". I can imagine that 醤玉子 refers to the boiled egg that is submerged in soy sauce. How do you read it though? I assume it's read "shoutamago".
I tried entering it into jisho.org, and it says "hishio tamago". This translation, however, is not a direct translation of 醤玉子. It's more of a translation of 醤 and 玉子 stuck together.
In English, we can make words up and its meaning can be inferred from the parts. An example would be soy-egg. That only works, since there's only one way to spell and pronounce soy and egg. I can infer the meaning of 醤玉子, which I hope I understood correctly, but I am not quite sure how to go about reading these agglomerations.