With reference to an earlier discussion about 'Over-Egging the Pudding', the Egg in question means to agitate or excite (from Anglo-Saxon eggian). The word only means urge or incite as applied to people. Furthermore the pudding in question probably refers to the entrails of animal, often made into pies, sausages etc. Indeed 'Pudding' appears to derive from a french word meaning a kind of sausage. Thus would not contain egg at all.