Srinagar, June 3 -- Haleema doesn't speak right away. She stands at the edge of the shrine courtyard, eyes closed, breath slow. The sounds around her-chants, whispers, a bazar bustle-blend into silence. She holds a copper bowl filled with rose petals. Her other hand clutches her daughter's arm.

"I've been coming here since I was a little girl," she says finally, opening her eyes. "Except for a few difficult years, I've rarely missed this day."

She is 87 now. And for nearly 70 times in her life, she is back at Khanqah-e-Moula, a centuries-old wooden shrine built along the Jhelum River in Srinagar's old city.

It's the 660th Urs of Mir Syed Ali Hamadani [RA], the 14th-century Persian saint who brought Islam to Kashmir, and transformed muc...