Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
In the bowl of a stand mixer, combine the very soft butter, brown sugar and vanilla and stir until blended. For a light and cakey cookie, beat until light and creamy. For a cakey but slightly heavier texture (my preference) just beat until blended. Scrape the bowl well, then add the egg and stir until blended. Scrape bowl and stir in the applesauce.
In a second bowl, stir together the flour, baking soda, salt and spices. Stir the flour mixture into the applesauce mixture, then stir in the oats, raisins and walnuts. The dough should be thick enough to scoop. If for some reason it's not, cover bowl and chill for 20 minutes.
Scoop cookie dough with a large cookie scoop onto the baking sheet, spacing about 3 inches apart. Bake one sheet at a time for 350 degrees F for about 15 minutes. If you are making the cookies smaller, check at 10.
Let cookies cool on the baking sheet for about 5 minutes, then transfer to a wire rack and let cool completely. These cookies actually improve a bit as they sit.