In the jutting chin of the Appalachians, near Alabama’s mineral-rich Red Mountain, men made the pig iron that girded America’s industrial revolution. The city that appeared around them, almost out of nowhere, exploded from about 3,000 people in 1880 to 26,000 just a decade later. By the early 1900s, city stakeholders had christened Birmingham, Ala., “the Magic City”—and the moniker stuck. Even now, the name of seemingly every business in town, from Magic City Pet Care to Magic City Law, recalls those boomtown roots.

These...