This is what I found in Wikipedia in addition to a page full of photos of Cotechino and lentils that came up on Bing.
I think you are safe on the head cheese issue. There was none mentioned anywhere I looked.
The cotechino (/ˌkoʊtɪˈkiːnoʊ, -teɪˈ-/, Italian: [koteˈkiːno]) is an Italian large pork sausage requiring slow cooking; usually it is simmered at low heat for several hours.[1] Its name comes from cotica (rind), but it may take different names in the different production areas. According to tradition, it is served with lentils on New Year's Eve,[2] because lentils—due to their shape—are 'credited' to bring money for the coming year.
It is prepared by filling the natural casing with rind, pork meat (usually of secondary choice), and fat mixed with salt and spices;[2] in industrial production, nitrites and nitrates are added as preservatives. Some similar sausages exist in the Italian cooking tradition, for example musetto and zampone which are made with different meat and parts of the pig, musetto being made with meat taken from the pig's muzzle and zampone being held together by the pig's anterior leg skin.