design before you build :)
one way is to raise your terrain up in a (ring, square, etc) and use that as your grounding for the walls, roof/floor across it and go down into it, that is your basement.
another way is just to dig it out like you did, but you need to have planned for this so you can ensure your support is good for it.
basically, you can't do a basement under a home that uses the middle part of the ground in some ways as support. You have to do ALL your support off outer walls if you go that route.
Not using any middle support limits your total height a little bit. Less than you might think, but its still a few tiles lost when you push the loading out instead of straight down.