This is the first occasion of its kind in Mr. Ashkenazy’s career. It is not a master class—he has never given one—but an event that will shed light on this technically demanding staple of the piano repertoire. During the event, the maestro will first demonstrate how the orchestra and soloist collaborate in rehearsal to create an optimal performance of the concerto, and then allow the up-and-coming Mr. Hong—chosen earlier this year by competition—to perform the piece in a more formal presentation, so that he has the opportunity to shine on his own. Following the performance, Juilliard’s provost and dean, Ara Guzelimian, will moderate audience questions for Mr. Ashkenazy and Hong Xu.

Mr. Ashkenazy brings a rich history of experience to the technically daunting but ravishing “Rach 3,” as the concerto is informally known by pianists. In a recent phone interview from his home in Switzerland, he explained that he first played the work at his graduation recital at the Moscow Conservatory. “It took me years and years to bring justice to the piece, because it is not made for my hands—they are small,” he said. “Although it is a very difficult piece, it is unbelievably pianistic,” meaning that the chordal and melodic elements of the solo piano part fit naturally with the pianist’s hands.

Mr. Ashkenazy, 70, has performed the Third Concerto some 50 times under some of the world’s great conductors, and has recorded the work five times—perhaps more than any other pianist. Four of those recordings feature Mr. Ashkenazy at the keyboard—under the batons of Eugene Ormandy, Anatole Fistoulari, André Previn, and Bernard Haitink. In his most recent recording, Mr. Ashkenazy conducts the Cleveland Orchestra with pianist Jean-Yves Thibaudet. And what advantage does this wealth of pianistic experience bring to Mr. Ashkenazy’s conducting of the Rachmaninoff Third? “One very important thing: I know every bloody note,” he says. “And I know how the pianist feels.”

Adding to the mix of factors on September 23 is Mr. Ashkenazy’s ongoing work with today’s young musicians. As the conductor of the European Youth Orchestra—an ensemble comprising musicians aged 14 to 24—Mr. Ashkenazy finds tremendous joy making music with pre-professional artists such as those he will find at Juilliard. The maestro notes that when he works with students, his approach is the same as the one he adopts when working with professionals. “I don’t do anything different with young people. They are much easier to work with because they want to be there. The level of the European Youth Orchestra is so high; it is like a professional orchestra.”

Mr. Ashkenazy’s audience at Juilliard on September 23 will be able to experience a fortunate confluence of Ashkenazy’s prolific knowledge of “Rach 3,” commitment to mentoring young artists, and consummate artistry. Sergei Rachmaninoff chose New York for the world premiere of his Third Concerto in 1909. And we are grateful that Mr. Ashkenazy has also selected New York—and Juilliard—to mark a first-time endeavor with conservatory musicians.