LONDON — “Work from your shoulder blades,” Steven Hoggett shouted as six performers swirled across the stage at the Palace Theater here. “Soften your left hand, wrists like chewing gum snapping back! Puff up your throat, like an angry bird!”

The six men puffing up their throats like angry birds were not dancers. They were actors, rehearsing a scene in “Harry Potter and the Cursed Child,” the theatrical extension of J.K. Rowling’s Harry Potter franchise that opened to rapturous reviews in London in 2016. This April it arrived on Broadway, receiving 10 Tony Award nominations and winning six.

Mr. Hoggett, nominated for best choreography — “Cursed Child” was the only nonmusical in that category — did not win the Tony. (That went to Justin Peck for the more traditionally dance-heavy “Carousel.”) But the recognition was well deserved: His choreography and movement direction for the two-part “Cursed Child” is no less meticulous and detailed than any dance number, and as important to the theatrical language of the play as the writing, by Jack Thorne, and the direction, by John Tiffany.

Unlike the movie versions of the seven Harry Potter novels, “Cursed Child” does not employ C.G.I., stunt people or elaborate special effects. Instead, the play’s magic, in both the theatrical and the literal sense, comes from the way swirling capes, moving staircases, fast scene changes and miraculously quick switches of identity (and costume) keep the story and the imagery in a constant flow of motion.