Learn Farsi: اینکه ما یک جد مشترک داریم خیلی جالب است. - The fact that we have a shared ancestor is very interesting.

inke literally means "this that," but it is used to mean "the fact that." Here, it turns the entire phrase ma yek jadd-e moshtarak darim (we have a shared ancestor) into a giant noun. That whole nominal clause acts as the subject of the main sentence: "[The fact that we have a shared ancestor] is very interesting."

Why is inke written as one word (اینکه) instead of two (این که)?

You will see it written both ways in Farsi. Whether it is attached (اینکه) or separate (این که), it is completely correct and pronounced exactly the same. When used as a single conjunction meaning "the fact that," writers often prefer to join the words.

Does having a long clause as the subject change the overall word order?

No, the standard Farsi word order still applies! The entire clause starting with inke acts as the Subject. The verb inside that clause (darim) sits at the end of its own mini-sentence. Then we have the main complement kheyli jaleb (very interesting), and finally the main sentence verb ast (is) goes at the very end of the whole sentence.

As a quick refresher, why is there no ezāfe linking yek (a) to jadd (ancestor)?

The word yek comes before the noun it modifies and does not take an ezāfe. The ezāfe only appears between the noun and its following adjectives. This is why we say (a ancestor-[ezāfe] shared), rather than linking with an .