To be fair (not that one particularly wants to) I suspect the word "essence" is used in the traditional philosophical meaning of "essentia", rather than in a smelly sense. As defined by Wikipedia:
"Aristotle made a distinction between the essential and accidental properties of a thing. For example, a chair can be made of wood or metal, but this is accidental to its being a chair: that is, it is still a chair regardless of the material from which it is made. To put this in technical terms, an accident is a property which has no necessary connection to the essence of the thing being described.
To take another example, all bachelors are unmarried: this is a necessary or essential property of what it means to be a bachelor. A particular bachelor may have brown hair, but this would be a property particular to that individual, and with respect to his bachelorhood it would be an accidental property. And this distinction is independent of experimental verification: even if for some reason all the unmarried men with non-brown hair were killed, and every single existent bachelor had brown hair, the property of having brown hair would still be accidental, since it would still be logically possible for a bachelor to have hair of another color.
The nine kinds of accidents according to Aristotle are quantity, quality, relation, habitus, time, location, situation (or position), action, and passion ("being acted on"). Together with "substance", these nine kinds of accidents constitute the ten fundamental categories of Aristotle's ontology."
I suppose you could twist this kind of reasoning to argue that genitals are an accidental property (like brown hair to the essence of being a bachelor), and that there is some deeper kind of womanhood which does not depend on female genitals or an experience of growing up as a female. Whether you choose to believe it is, of course, a different matter...