Hanabira mochi is synonymous with New Year and commonly eaten in January. It is unique in that folded inside the thin layer of mochi are miso paste and a stick of gobou (burdock root), two ingredients not commonly associated with sweets.
One theory for this curious choice or ingredients goes all the way back to Heian period (7th - 12th century) when the Imperial Court held a ceremony in the beginning of the year called "Hagatame no Gishiki." Translated as "tooth hardening ceremony" they would eat hard food, such as daikon radish and salted ayu sweetfish, to pray for longevity.
During the Edo period (16th - 18th century), hanabira mochi was given as an offering to the Imperial Court. According to historical record, it was a thin round white mochi topped with a red mochi and ayu sweetfish. This would then be gradually simplified by replacing the ayu sweetfish with gobou (burdock root).
In the Meiji era (1868-1912), the 11th head of the Urasenke School of Tea, Gengensai, received permission from the Imperial Court to serve hanabira mochi during "Hatsugama" (first tea ceremony of the year). Ever since then, confectioners throughout Japan started making hanabira mochi every January.
Our version of hanabira mochi is called Gosho Kagami, named so due to our proximity or the Kyoto Imperial Palace (Gosho). If you happen to be in Japan during New Year, make sure to give it a try.