Catalyzes the oxidative sulfurization of hercynine (N-alpha,N-alpha,N-alpha-trimethyl-L-histidine) into hercynyl-gamma-L-glutamyl-L-cysteine sulfoxide, a step in the biosynthesis pathway of ergothioneine (ERG) (By similarity). ERG is one of the major redox buffers which protects bacteria against redox stressors and antibiotics; loss of ERG or mycothiol (MSH, the other major redox buffer in this bacteria) leads to respiratory alterations and bioenergetic deficiencies that negatively impact virulence (PubMed:26774486). gamma-L-glutamyl-L-cysteine + hercynine + O2 = gamma-L-glutamyl-hercynylcysteine S-oxide + H2O Amino-acid biosynthesis; ergothioneine biosynthesis. Expressed in log phase, part of the egtA-egtB-egtC-egtD operon, which does not include egtE (PubMed:26774486). Belongs to the EgtB family.