Line two 8" cake pans with parchment paper and spray with non-stick spray. Mix cake mix with eggs, water, pudding mix and applesauce. Fold in ground pecans and chopped pecans. Pour evenly into pans. Bake according to package mix directions till toothpick comes out clean.
Cool 10 minutes in pans then transfer to wire racks and cool completely.
Mix butter and vanilla. Add confectioners sugar, 1 cup at a time and mix in completely. Add pinch of salt and rum to desired consistency.
Frost cake. Press chopped pecans into sides of cake and garnish top with pecan halves.