Peziza domiciliana, the House Cup Mushroom!
A rather unusual higher fungus, in that it's perfectly happy to grow large fruiting bodies inside your house. Indeed, householders can be quite surprised to find these these sprouting suddenly from plaster, cement, sand, gravel, coal dust,in your fireplace, and so on. I found a large stand of the things growing from the carpet in a client's converted carport once, but it also grows in cellars, greenhouses, shower stalls, damp closets, under porches, on wet rugs, behind refrigerators, around leaky water beds and inside your car. ( thankyou Wayne's Word )
Below is Youtube video of the latter possibility - the Witch's Butter ID is dubious, but then amateur mycology is cursed by dodgy common names and misidentifications
They're not very fussy about what they eat, although damp carpet is a favourite, and as Arjuna points out in the post they grow fast once they're ready to spore. Many mushrooms do sprout fast, because they're using osmotic pressure to inflate a fruiting body they prepared earlier. It's a surprisingly powerful mechanism, easily capable of punching a delicate toadstool up through asphalt. As to whether you can eat them, I wouldn't risk it. Certainly there are edible cup mushrooms, and even edible Pezizas, but testing the edibility of a mushroom can backfire horribly when the poison kills you a week after you eat it. Especially if you've misidentified the mushroom in the first place - Destroying Angel and the other Death Caps are all too easily mistaken for button mushrooms, horse mushrooms, and edible puffballs - a trifecta of horrible demise. Or then there's Coprinopsis atramentaria, the Common Inkcap, or Tippler's Bane. Edible... unless you drink alcohol with your meal, in which case it poisons you by completely disabling your alcohol dehydrogenase enzyme.
Peziza is an Ascomycete - a highly successful group of fungi that includes morels, truffles, brewer's yeast and baker's yeast, Dead Man's Fingers, and the majority of lichens. A good number are plant diseases, and one is very famous indeed - Penicillium. Unlike the 'normal' gilled mushrooms, the spores of the cup mushrooms and morels are grown on the upper surface of the mushroom, to be dislodged by rain or wind.
But anyway, that's Peziza domiciliana - and may all your House 'Shrooms be big ones.