As for Broadway, I really hope that they can do a revival of Kismet (an old Classical musical) and do a revamping of it. It's set in Baghdad, and would be a perfect opportunity to cast Indian, Arab, etc. Perhaps Ramin Karimloo who is Iranian could be in it.
As for Asians, they have a more shows than lets say Latinos like myself.
Pacific Overtures, King and I, Miss Saigon, Flower Drum Song, Allegiances, Here Lies Love, Chinglish, Yellow Face, M. Butterfly, etc.
For Middle Easterners/South Asian, um Aladdin? and Kismet.
Then all of us minorites have the few cameo roles in plays.