Crunchy Oreo cookies. Thick peppermint ice cream. Rich fudge sauce. More cookies. Dissected into parts, the Bauder’s peppermint bar, a famed Iowa State Fair ice cream novelty, may seem simple.

In response to fans of the flavor imploring the brand to make this a year-round item in the ice cream’s reviews, Häagen-Dazs has said that the peppermint bark ice cream products are limited ...