I don't know much about mushrooms, except that the ones you have are caused by overly-wet soil. Your veggies are in plastic containers - you may need to drill some extra drainage holes near the bottom. Do not water so often - wait until the soil dries out a bit first. Also, is that wood mulch? You should not use wood chip mulch on veggie beds - it is too acidic for veggies; try straw (not hay) instead.

I assume you want to harvest veggies, so I suggest removing the mushrooms and not water until the soil feels dry (or the plants start to wilt). If the mushrooms come back you are definitely over-watering and your veggies will probably die.

Possibly Coprinellus flocculosus, an Ink Cap mushroom.