The hanabiramochi (葩餅) is filled with symbolism for the New Year.
The reddish pink is not only a celebratory colour, but hints at ume blossoms (梅) and their associations with renewal. The burdock, representing ayu (アユ/鮎 'sweetfish'), is a wish for long life.

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Plum blossoms are a symbol of renewal and so feature heavily in motifs around the new year period.

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Woodblock print of ume blossoms.
Image thanks - https://ukiyo-e.org/

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Burdock in hanabiramochi represents sweetfish, symbol of long life. Traditionally the fish were eaten in New Year banquets as good luck for the upcoming year.

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Hanabiramochi, a sweet typically eaten at the start of the year.