FOR YEARS NOW, Vietnam has been the world’s second-largest coffee exporter, according to the International Coffee Organization. And yet, for all the fervor over single-origin beans from Central America and Africa, third-wave-coffee culture has been slow to embrace Vietnamese product.

That’s finally changing. Cafes specializing in Vietnamese coffee now caffeinate cities from Pittsburgh to Austin. Pop-ups such as Kasama Cà Phê in San Francisco are handling beans from Vietnam with respect and showcasing their flavors in hot and...