Six years ago, a group of Chinese engineers took on a daring challenge: turning what others saw as useless waste into something valuable. Their target was the large amounts of low-grade nickel and cobalt ore found on remote Indonesian islands. These ores were previously considered too poor in quality to be worth much. But if these engineers could figure out how to process them, they could unlock a new source of crucial minerals needed for electric-vehicle batteries.

The method they aimed...