。
How would you like the eggs cooked?
Literal
Egg [topic-は] how cook-humbly-shall-I-[question-か].
いたします is the humble (謙譲語) form of する — the speaker is lowering themselves to elevate the listener. Typical of restaurant waitstaff, hotel staff, or any keigo context where the speaker serves the listener. The whole sentence is one politeness step up (調理しましょうか).