Melt the butter in a saucepan large enough to accommodate the apples. Add the apples and saute over medium-low heat until the apples start to soften. Add the reserved cider, apple cider and cinnamon and cook over low-medium heat until most of the cider has evaporated and the apples are cooked and very soft.

Add the heavy cream and walnuts and cook until the cream has reduced by half. The end result should be a very chunky, sweet/savory applesauce.