Turn acorn squash upside down on cookie sheet. Bake until it begins to soften, about 30-45 minutes.
Remove squash from the oven and turn onto a plate so that the flesh is facing upwards. Place butter and brown sugar into the squash, and place remaining squash over the other piece (Put in a baking dish so it doesn't slide while baking).
Place squash in the oven and bake another 30 minutes.