Professor Henry Higgins turns Eliza Doolittle, an unkempt Cockney flower vendor, into an elegant lady in the many versions of George Bernard Shaw’s Pygmalion. Who can forget Rex Harrison and Audrey Hepburn in My Fair Lady, the magnificent film musical based on this classic? In Mickey Blue Eyes, a similar challenge faces James Caan. He plays a mob-connected owner of a New York Italian restaurant whose daughter (Jeanne Tripplehorn) falls for a very, very British art auctioneer (Hugh Grant). After an accidental killing takes place, Caan needs Grant’s assistance to outwit his enemies. But first he must teach the awkward Englishman how to act like a “made man.”

Compared to Caan’s problems, Professor Higgins’ task seems as simple as pouring a cup of tea. When Grant mumbles his wiseguy lingo, he’s a cross between Monty Python’s John Cleese and Benny Hill. When he passes himself off as a tough guy, he’s more Mickey Mouse than Mickey Blue Eyes (his fake gangster moniker). Grant is quite funny in these well-written scenes, mostly because he treats everything so seriously.

Director Kelly Makin (Brain Candy) admits being attracted to the script because of Grant’s involvement in the project. “You could just see Hugh in this role, in these situations. There’s nothing better than Hugh Grant backed into a corner,” says the talented Canadian filmmaker. Grant himself worked on the screenplay for two years with writers Adam Scheinman and Robert Kuhn. The whole story was molded for this popular star of such hits as Four Weddings and a Funeral and Notting Hill. These efforts paid off handsomely, giving Grant the chance to deliver one of his best performances ever.

Other members of the cast shine in their roles too. Tripplehorn (Waterworld), usually seen in dramas, shows an excellent flair for comedy as a woman who fears the man she loves will be corrupted by her father and his associates. Together, this stunning actress and the boyishly handsome Grant generate plenty of on-screen sparks and humor. Caan (The Godfather, This Is My Father) almost steals the film as Tripplehorn’s Mafia-burdened father. His rendition of “You’re Nobody ‘Til Somebody Loves You” left me hungry for more. As a godfather figure who ventures into the New York art world, Burt Young (Rocky) makes his role come to life with surprising authenticity. James Fox (Remains of the Day) does the same with his portrayal of an auction house owner described by Grant as “the most English and the nicest man in the world.”

Like so many other films, including Analyze This, The Freshman, and Jane Austen’s Mafia, this romantic comedy pokes fun at gangsters and Italian stereotypes. But Mickey Blue Eyes boasts a new twist and performances it would be a crime to miss. Now that’s an entertainment offer you can’t refuse.

(Released by Castle Rock Entertainment/Simian Films and rated “PG-13” for brief strong language, some violence and sensuality.)