Every year in the third week of March, Manijeh Irani, 64, makes a tour of the markets of her adopted city, Mumbai—grocery stores, stalls of fresh and dried fruit, sweet shops, even an aquarium—for goods to adorn her festive table for Nowruz, the Persian New Year.

Nowruz (”new day”) is pegged to the Northern Hemisphere’s vernal equinox and symbolizes the upswing of the forces of light and life after the dark cold days of winter; it is one of humanity’s oldest holidays. In Tehran, where Mrs. Irani spent the first 18 years of...