My Romance (m. Richard Rodgers, w. Lorenz Hart) was introduced in the Broadway extravaganza Jumbo, in which it was sung by Donald Novis and Gloria Grafton. The musical opened on Broadway at the Hippodrome Theatre on November 16, 1935 and closed on April 18, 1936 after 233 performances. Directed by John Murray Anderson and George Abbott it starred Jimmy Durante and a number of circus specialty acts. Jumbo tells the story of a financially-strapped circus. At the end of each performance, Durante lay down on the stage and permitted a live elephant to place its foot upon his head.
The large 5,000 seat theatre was turned into a circus tent where the various specialty acts (including acrobats and animal acts) performed during the show. The music was played by Paul Whiteman and his orchestra.  – Wikipedia extract, adapted
Mel Tormé – A date is not given; but the video provider attaches the following information about the singer
Mel Tormé was…best known for his classic jazz vocals. He was also a jazz composer and arranger, a drummer, an actor in radio, film, and television, and the author of five books. He co-wrote the classic holiday song “The Christmas Song” (“Chestnuts Roasting On An Open Fire”) with Bob Wells. His 1949 composition “California Suite,” became Capitol Records first 12-inch LP album. His singing at New York’s Copacabana led a local disc jockey to give him the nickname “The Velvet Fog”. This selection is from his album Thats All.
Ben Webster – Recorded: Live at De Hertenkamp Laren, The Netherlands September 2, 1970 — Personnel: Ben Webster – Tenor Sax, Cees Slinger – Piano, Rob Langeris – Bass, John Engels – Drums
Bill Evans Trio — live, 30 January 1979, at The Maintenance Shop in Ames, Iowa (Iowa State University)
Bill Evans – piano
Marc Johnson – bass
Joe LaBarbera – drums
John McLaughlin and Chick Corea – date unknown
Carly Simon – The title song and first track of a Simon album released on 22 Feb 1990
live c. 1990 at an Arista Records event
Jacques Lautier Quartet – 1993
The provider, Jacques, says (followed by my translation)
Un très beau morceau de Rodgers et Hart que j’interprète avec mon Quartet composé de Petro Garces à la basse, Marc Andreis à la batterie, Marcel Volberg aux percussions et moi-même Jacques Lautier au piano. Cela a été enregistré lors d’un concert au Club Frédirique de Vallauris le 11 novembre 1993.
A very beautiful piece by Rodgers and Hart that I interpret with my Quartet composed of Petro Garces (bass), Marc Andreis (drums), Marcel Volberg (percussion) and myself Jacques Lautier (piano). It was recorded during a concert at the Club Frédirique de Vallauris, 11 November 1993.
David Matthews and Friends, a group of musicians from the Manhattan Jazz Orchestra. I can always count on this band for the finale.