Mark Rylance, routinely described, at 53, as the greatest English theater actor of his generation, is the galvanizing, unmissable actor other actors flock to see. What a treat we have in store! The two-time Tony Award winner is starring on Broadway in the Shakespeare’s Globe productions of Twelfth Night and Richard III (opening in repertory at the Belasco, November 10).

Rylance’s Tony-winning performances revealed his astonishing virtuosity. In 2008 he turned a failed retro farce, Boeing-Boeing, into a hit with his hapless innocent, Robert from Wisconsin: a quiet riot in the spirit of Buster Keaton. In 2011 he was Johnny “Rooster” Byron, the mesmerizing wild gypsy in Jez Butterworth’s state-of-England drama, Jerusalem.

In Richard III, he even dares to make the hunchbacked king—history’s gleeful psychopath and “shadow in the sun”—surprisingly funny. (Until he freezes our laughter.) Why, I asked him, do we relish Richard’s monstrous nature so much? “Because we are all capable of monstrosity?” he suggested.

A gentle eccentric offstage, Rylance was the first artistic director of the Globe, on London’s South Bank (1995–2005), and he returned the company to its Shakespearean tradition of casting males as women. What’s the difference, I asked, between playing a woman and a man? “Sex,” he replied.

He plays the lovesick Lady Olivia in Twelfth Night. No problem! He’s already played Cleopatra.