Diljit Dosanjh is one of India’s biggest stars. Now he’s taking on America.

When I first met Diljit Dosanjh in 2017, he was a rapidly rising star in India. His Hindi film debut, Udta Punjab, was all the rage, only a year after his Sardaar Ji became one of the top-grossing Punjabi films of all time. His single “Do You Know,” a slow jam-esque love song, was an enormous hit. He served as judge of a reality TV singing show and had an international tour in the works. “I have barely begun,” he told me then. “This is nothing.” 

Now, seven years later, the 40-year-old...