It's most likely a pelican; they often look a bit like falcons in medieval art. The lore was that they would pierce their own breast to feed the chicks with their blood, which was understood as analogy for Christ's self-sacrifice and the blood of the Eucharist. (Architectural term is a roof boss.)
Thank you, that is so interesting!
Here's another example from the late Middle Ages: the pelican often appears with three chicks at their feet, curling their necks forward to reach their breast; I can imagine the missing part of the Canterbury roof boss might have also included a long, thin neck like this, which would break easily.
