Geometric Langlands can be interpreted as a mirror symmetry between the moduli space of Higgs bundle of group $G$ via the same moduli space of its Langlands dual $G'$. Once we consider the insertion as a form of parabolic structure or more generally coadjoint orbit, it is clear that the conjectural mirror symmetry of moduli space of Higgs bundle requires a version of mirror symmetry between coadjoint orbits. In the talk, we will explore the possible "coadjoint orbit mirror symmetry".