Rafadan yumurta mı güzeldir, hazırlop yumurta mı?

I understand that -mi, as a participle, makes the word before it a question. And I can probably figure out the context if its after a time span word:

Gelecek hafta mı?

And if its before an adjective:

Arabayı kırımızı mı?

Or if before a question word: (do you even need tp include it for these?)

Kim mi?

However, I can´t see how the participle makes the preceding noun (soft-boiled egg) into a question since an adjective follows (güzeldir)

Then for the other half, -mi? is last. So I don´t know how to read that except as "is he a hard-boiled egg?"

Mind you, this is not my sentence. Its an example from FSI Turkish website. But to answer it for practice, I want to understand the structure of this sentence. thanks always

While you wait for an expert, here are my thoughts 

Rafadan yumurta mı güzeldir, hazırlop yumurta mı?

Is it the soft-boiled egg or the hard-boiled egg that is nice?

As a learner I think this question could also be written this way 

 Rafadan yumurta mı yoksa hazırlop yurmurta mı güzeldir?

First, a small correction:

Particle not participle.

Take a simple sentence for example:

Özne Nesne Eylem = Subj Verb Obj

Özne mi Nesne Eylem = Is it Subj that/who Verb Obj

Özne Nesne mi Eylem = Is it Obj that/whom Subj Verb

Özne Nesne Eylem mi = Axulalry Subj Verb Obj (Typical question format in English)

Özne (Subj) = Ali

Nesne (Obj)  = Elif´i

Eylem (Verb) = seviyor

Ali Elif´i seviyor = Ali loves Elif

Ali mi Elif´i seviyor? = Is it Ali who loves Elif?

Ali Elif´i mi seviyor? = Is it Elif whom Ali loves?

Ali Elif´i seviyor mu? = Does Ali loves Elif?

"Kim mi?" is possible. It usually happens when somebody asks you "kim? = who?" and you ask back "who?"? ((why) Do you ask "who?"?).

Thank you Henry and Si+ I am begining to understand now.