When cooking whole, halved, or quartered acorn squash pieces, I’ll usually only peel it after cooking since it’s really easy to remove then. However, if you want to peel it before cooking, there are several ways. Option one is to use a sharp knife to work your way around the squash from top (by the stem) to bottom, slicing away strips. This method will also remove some of the squash flesh, though. Option two is to lightly cook it. You can do this either in the microwave (for around 3 ½-4 minutes, poke holes in the veg first) or boil the whole squash for 12-15 minutes. Once it cools enough to handle, simply peel away the skin.