Wash and then pierce potatoes with a fork. Do not grease or wrap in foil. Bake for 1 hour at 400°F. When potatoes are just about done, wash and chop mushrooms and sauté them in the butter or margarine. Remove potatoes from the oven, hold them in your hand with a pot holder and cut away the top. Remove the potato insides, being careful to keep the skin whole. Combine the potato pulp with the salt, pepper, apple sauce and yogurt and mash until fluffy with no lumps. Then add sauteéd mushrooms. Put this mixture back into the potato skin. It will fill the skin and be mounded on the top. Press the cheese square into the center of the top. Bake 20 minutes more at 300°F to heat through.