Stand the squash on the large end. Use a large knife or cleaver and cut in half from the stem to the bottom. If you have a rubber mallet, you can use it to tap the blunt side of the blade to help push the knife through the squash. Place the cut sides down on the prepared baking sheet and roast until the skin can be easily pierced with a knife, about 45 minutes.
Remove from oven and set aside until it is cool enough to handle. Use a spoon to scoop out the flesh and put it into a bowl. Mash with a potato masher.
In the sauce pan, melt the butter and milk together for about 1 minute. Mixture should be hot, but not boiling. Add the mashed squash and stir well. Add the ginger and stir. Continue cooking over low heat until the squash is heated through. Salt and pepper to taste and serve immediately.