I read some of it, and after you mentioning it, I read some more. E.g. The Bedrock of Fairness touches on the issue of whether or there is this moral 'essence'. Also, I liked Paul Graham's What you can's say, which discusses the way morals change.

Overall, I think the closest thing that comes to a 'moral essence' is that the set of moral intuitions (no matter how vaguely defined) is the best thing that evolutionary processes have been able to come up with. Hume's is-ought problem does not really apply because there is no real ought.

The set of morals we ended up with is probably best summarized with the Golden Rule, which is a useful illusion in the same way that free will is, and similarly, for all practical purpose we can treat it as if it were real.

[ It's an interesting though experiment to consider whether there could be other, radically different sets of morals that would lead to the same or better evolutionary fitness, while still being 'evolutionary feasible'. ]