You can't and aren't supposed to. You used to be able to before the update to V3 and the introduction of Spoiled eggs, so that might be why you see a few eggs in shops, but now you can't.
If you'd like to sell your eggs, you can list them in the Egg Market. If you put your mouse over Shops at the top of the page, the last link under it you'll see is the Egg Market.