The American metaphor for a humiliating apology, eating (boiled) crow, has a much older British equivalent, eating humble pie. Both the boiled crow and the dubious ingredients of this pie imply a poor man's meal, thus adding the element of humility to the mix. A person who loses a particularly high wager or loses credibility after boasting or bragging is most likely doomed to eat a metaphorical serving of humble pie as penance.
The origin of the expression humble pie can be traced back to the Middle Ages, although the association with humility or painful humiliation is not so direct. Following a hunt, the innards of the slain animal would often be baked into a meat pie and served to servants or others of low social standing. These organs and other offal were originally called numbles, but over time the common reference changed from "a numble" to "an umble," thus rendering the meat dish as "an umble pie."
Due to the fact that umble pies were primarily served to the most humble of servants, a connection developed between the consumption of a dubious but filling dish and a true sense of humility. The word "humble" in the metaphorical pie comes from the Latin humilis, meaning "from the earth," while the "numble" or "umble" in an actual umble pie comes from French and Old English words meaning "loin." Dropping the initial H sound from certain words is a common practice in certain British dialects.
Eating humble pie is meant to be a metaphorical punishment for excessive arrogance or boasting. Few people would ever eat such a dish voluntarily, but others may wish that particularly self-important public figures or abusive employers would take a bite or two, especially when they are proven wrong in a very public way. Eating humble pie should take the offender down a few pegs on a social or professional ladder, at least long enough to feel humbled or properly chastised for his or her overbearing behavior.
There are recipes available online and in research cookbooks for actual humble pie, although the ingredient list may be difficult to obtain in standard grocery stores. There are also fictitious "recipes" for creating a metaphorical humble pie, including dashes of apologies, cups of forgiveness, a pinch of humility and so on. The important thing to remember about humble pie is knowing when it needs to be served, and who deserves to get the biggest slice.