When Tracy Britt arrived in Omaha, Neb., in 2009 to meet with Warren Buffett, she brought a Harvard M.B.A., a glittering resume and a boatload of ambition. But she also brought the famed investor a gift to highlight their shared Midwestern roots: a bushel of corn and a batch of tomatoes.

The seed Ms. Britt planted that day yielded quick results: a job for Ms. Britt as Mr. Buffett's financial assistant at Berkshire Hathaway Inc. Almost four years later, it has blossomed further, with Ms. Britt emerging as one of Mr. Buffett's...