To do justice to such a beloved figure may seem impossible, but one young actor—and one filmmaker on a hot streak—just rose to the challenge.

The Anthony Bourdain biopic “Tony” explores a pivotal summer in 1975 when the future chef-traveler worked in a Cape Cod kitchen.

Also starring Antonio Banderas, Emilia Jones and Leo Woodall, Matt Johnson’s bio-drama chronicles a formative Provincetown summer during which the future chef worked in a hectic…