I learned that mujhe is more like "to me" or "for me". So the sentence would be literally translated "For me eggs are wanted." Eggs becomes the subject, not the one wanting them.
Why mujhe instead of main?
That's the sentence form when चाहिए is used, object pronouns instead of subject pronouns. तुम्हें अंडे चाहिए - You want eggs.
Ah so it's similar to Spanish (gustar) in that my breakfast desires are seen as affecting me rather than the eggs?
And so the plot thickens with two more important new words!
I want egges
should ka bhi matlb (chaiye) hota hai