Socrates talked. The assumption behind his approach to philosophy, and the approaches of millions of people since, is that moral thinking is mostly a matter of reason and deliberation: Think through moral problems. Find a just principle. Apply it.
But this is not very Socratic at all. For Socrates, morality is a craft or skill, analogous to shoe-making or medicine, and just as it would be odd to characterize the craft of a physician by saying "Think through medical problems, find a healthy principle, apply it," so it would be odd to characterize the Socratic approach to moral thinking in these terms. And Socrates pretty clearly denies that moral thinking is mostly a matter of reason and deliberation; rather, it is knowing how to live, which makes use of reason and deliberation but is not "mostly" reason and deliberation. And in fact, thinking through moral problems is itself not a major part of Socratic discussion of morality.
Nor, outside a handful of exceptions, like casuists and a few contemporary analytic philosophers, has it been a major part of philosophy. And even the casuists were writing confessor's manuals, which are primarily for evaluating matters after the fact and only secondarily and indirectly for deciding behavior before the fact; the real practical influence of casuistics was always intended to reside in the living practice of confession and spiritual direction. So I suppose the 'approaches of millions of people' is really 'approaches of a small handful of analytic philosophers in the past few decades', because that's about all it really covers.
The problem with sensationalism about the "evolutionary approach to morality" is that this is all business as usual. Nothing Brooks says was not already said more rigorously by Darwin in the nineteenth century, when he entered into the field of moral philosophy on the side of the moral sense theorists against the utilitarians; very little of that is much beyond what Hume had already said in the eighteenth century; and the basic point, of morality as being like aesthetics, we already find in Shaftesbury in the seventeenth. And one can probably trace it back further. There has been no sea change; only a gradual development of modern moral philosophy along a direction laid down centuries ago.