Almost definitely puffballs, one of my favorite mushrooms to forage. Though I've never had ones this big and I hear they lose a bit of flavor if they're giant.
If you cut a *(vertical) cross section and it's a uniform texture with nothing that looks like the structure of a classic capped mushroom that should rule out any lookalikes. Should still be good if the inside is white and not starting to turn brown.
We used to prepare and eat these back home. They're a bit like eggplant. My dad would sometimes hop out of the car on his commute home from work and grab these off the side of the road.
I'd think that you could build some sort of temperature/light/humidity controlled terrarium, model mushroom growth, and then grow mushrooms at the maximum that they're biologically able to grow.