HAMILTON, Mo.—This tiny farm town used to be known as the home of James Cash Penney Jr., founder of the namesake department store chain. These days, it is better known in some circles as the home of Jenny Doan.

Those would be quilting circles. Over the past few years, Mrs. Doan, 57 years old, has become a veritable superstar of the craft. Her YouTube tutorials on how to make quilts have drawn as many as a million viewers, some from as far away as South Africa.

...