Isiah Whitlock Jr. has played a corrupt state senator ("The Wire"), an ornery defense secretary ("Veep") and an uptight insurance agent ("Cedar Rapids"), but in the course of a distinguished television, movie and Broadway career, his most unexpected role by far has been…winemaker. For the past several years, Mr. Whitlock has been dabbling in Cabernet, Chardonnay and, most recently—and most ambitiously—Pinot Noir.

He produced the Cabernet and the Chardonnay in his Chelsea apartment. Specifically,...