We do have 'yule logs' which wikipedia tells me are broadly the same cake (chocolate sponge cake rolled up around frosting) but I don't know that it's really al

We do have 'yule logs' which wikipedia tells me are broadly the same cake (chocolate sponge cake rolled up around frosting) but I don't know that it's really all that common. US Christmas is stereotypically endless cookies, with gingerbread and cinnamon rolls coming in strong. In general though I think the culinary traditions aren't really unified enough to be worth talking about.