I had always assumed that a nest-egg (of the financial variety) was something that would hatch upon a rainy day. I made this mistake because I have never kept chickens.
Chickens, being giddy creatures, are liable to lay their eggs and then, when they have hatched, to abandon their nest. To stop this happening the solicitous gallicultist will slyly introduce a nest-egg. A nest egg is not an egg at all, but it looks like one and the chicken is fooled. She stays with the nest constantly hoping that the little fake will hatch. Whilst there, she lays more eggs of her own.
The metaphorical potential of a nest-egg that keeps the chicken laying was not lost upon Samuel Butler who in 1678 described a lawyer's office thus:
...mounted in his pew,
With books and money placed for shew,
Like nest-eggs to make clients lay;
And for his false opinion pay...
And from there it became the principal invested in a bank to produce dividends and interest. So, properly speaking, one should, if one wishes to maintain the metaphor and solvency, spend only the interest on your nest egg.
However, in matters financial one should always remember the words of George Best:
I spent a lot of money on booze, birds and fast cars. The rest I just squandered.
I too like chicken pie.