Preheat oven to 375°F. Line a cookie sheet with parchment paper or a silpat mat.
In a small bowl, mix together the applesauce and raisins. Set aside.
In a large bowl, using a hand or stand mixer, beat the brown sugar, butter, and egg until light and creamy, about 3 minutes. Fold in the applesauce and raisin mixture with a spatula. Set aside.
In a small bowl, whisk together the flour, salt, baking soda, cinnamon, nutmeg, and allspice. Add the flour mixture into the batter and beat until combined. Fold in the oatmeal and nuts with a spatula just until combined.
Drop cookie dough by spoon, about 2 inches apart on a cookie sheet. Bake for 10-12 minutes, until the tops no longer look wet and the sides darken a little in color.
Move the cookies to a rack to cool. Store covered at room temperature for best taste.