To easily peel the acorn squash without losing a lot of vegetable, gently drop the squash in a large pot of boiling water, and boil for 15 minutes. Pour off the boiling water and fill with cold water and let sit 5 minutes to cool. When cool enough to handle, use a knife to slice off the peel on the ridges and use a teaspoon to dig out the peel in the valleys. Slice the squash in half and remove the seeds and stem. Then slice the halves into sections and finally cut into 1 inch chunks.
Place the squash chunks into a large microwave-safe bowl along with the apples. Dot with pieces of butter. Sprinkle the brown sugar, walnuts, salt and cinnamon over the top. Cover with plastic wrap, and poke a few holes in it for ventilation.
Cook in the microwave for 7 1/2 minutes on full power. Remove, uncover, and stir. Return to the microwave, and cook for another 7 1/2 minutes on full power, until tender. Serve hot.