Preheat oven to 375 degrees F.
In a bowl, combine the dry ingredients and set aside.
In the bowl of a standing mixer, fitted with a paddle attachment, cream the butter. Add the brown sugar and continue creaming. Then add the eggs and applesauce mixing well. Gradually add the dry ingredients and raisins to make dough.
Drop by rounded tablespoons onto a greased cookie sheet (save those butter papers!) and bake until light golden brown, about 9 to13 minutes. The cookies do not brown very much. Sprinkle with powdered sugar.
Peel and core apples and cut into quarters. Place them in an enamel sauce pan with the water and lemon juice then bring to a boil then turn the heat down slightly and simmer 30 minutes to break them down and get them to thicken. Take off the heat and stir in the sugar and cinnamon, if using.