I am trying to figure what the name of the part of the eggplant where the stem is attached to. I heard it in the following video between 00:25-00:30: Baba Ghanoush - How to Make Roasted Eggplant Dip & Spread - YouTube
It sounds like “enable” but I am not sure how it is spelled. 
I think they’re saying “navels” and referring to the indentation on the bottom of the eggplant; it’s confusing because they talk about having the stem still attached, and I don’t see why that’s relevant when looking at the navels.
But anyway, I’m pretty sure they’re not referencing the stem parts but the elongated navels at the eggplants’ bottoms.
Yes, Chef John (love him, although his voice and inflections can grate on some people) says “navels” there.
I can’t really believe anyone who thinks there are “male” and “female” eggplants.
Yeah, that part appears to be some folk wisdom.
“The Name of Part of the Eggplant” sounds like an auto-translate of an Umberto Eco book.
For what it’s worth, the green leafy structure at the “stem end” of the eggplant is called the calyx, and each individual “leaf” is a sepal. They’re leftover structure from the flower that generated the fruit; see Wikipedia for more information.