Mutual recognition has two distinct senses.
The first is an ethical ideal with roots in Aristotle’s discussion of friendship and love, as generalized by Fichte, and especially Hegel. Brandom and others consider it central to the understanding of what Hegel was really trying to do. (See Mutual Recognition; Pippin on Mutual Recognition; Recognition; Kantian Respect; Hegel’s Ethical Innovation; Trust as a Principle).
The second is a nonreductive meta-ethical theory of how normativity or the “ought” in general comes to be. Such a theory was broadly suggested by Hegel, and has been recently developed in great detail by Brandom in A Spirit of Trust. It addresses the emergence of normativity, but bootstraps itself from within the domain of a clarified understanding of normativity itself. Other accounts of the emergence of normativity have generally explained it in terms of something else, effectively reducing the “ought” to some kind of facts.
While I don’t see how anyone could reasonably object to the ethical ideal, its meta-ethical elaboration into a “normative all the way down”, self-bootstrapping theory of the constitution of normativity is an extensive, highly original, many-faceted theoretical account building on the first that no one could be expected to fully grasp on merely hearing it mentioned. I think its combination of detail and coherence is an amazing and unprecedented accomplishment, confirming Brandom’s place among the greatest philosophers who could be counted on one hand, but it takes real work to assimilate. (For an overview, see Hegel’s Ethical Innovation.)