As many of the people who claim to have introduced the cookie to the United States are Japanese, the theory is that these bakers were modifying a cookie design they were aware of from their days in Japan.
Makoto Hagiwara of Golden Gate Park's Japanese Tea Garden in San Francisco is reported to have been the first person in the USA to have served the modern version of the cookie when he did so at the tea garden in the 1890s or early 1900s. The fortune cookies were made by a San Francisco bakery, Benkyodo.

Unusual non-positive aphorism found in a fortune cookie
David Jung, founder of the Hong Kong Noodle Company in Los Angeles, has made a competing claim that he invented the cookie in 1918. San Francisco's mock Court of Historical Review attempted to settle the dispute in 1983. During the proceedings, a fortune cookie was introduced as a key piece of evidence with a message reading, "S.F. Judge who rules for L.A. Not Very Smart Cookie".
A federal judge of the Court of Historical Review determined that the cookie originated with Hagiwara and the court ruled in favor of San Francisco. (wikipedia)
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