To over egg the pudding
to over state or exaggerate
e.g. I recently watched a documentary about the history of childhood, comparing and contrasting childhood over the centuries. It over egged the pudding with regards to how easy and comfortable it presented the experience of children today.
The idiom uses the fact that too much egg in baked goods causes them to turn out badly.
The earliest example of the phrase in print that I know of is from 1845 Robert Smith Surtees' novel Hillingdon Hall, 1845:
'We mustn't over-egg the pudding,' as the Yorkshire farmers say.