Preheat the oven to 350ºF (177ºC). Spray a 9X13-inch baking dish with nonstick cooking spray. Set aside.
Place raisins (3/4 cup) and 1 cup hot water in a small bowl; set aside.
In a large bowl, cream the butter (1/2 cup) and sugar (2 cups) until light and fluffy. Add eggs (2) and mix until combined.
In a medium mixing bowl, whisk together flour (2 cups), cinnamon (2 teaspoons), allspice (1 teaspoon), cloves (1/4 teaspoon), baking powder (1 teaspoon), baking soda (1 1/2 teaspoons), salt (1/2 teaspoon), and brown sugar (1 1/2 cups).
Add flour mixture to butter mixture, alternately with applesauce (1 1/2 cups) and 1/2 cup water. Mix until evenly combined.
Drain raisins and discard the soaking water; fold into batter with the pecans (1 1/2 cups).
Pour batter into the prepared baking dish. Bake until a toothpick inserted into the center comes out clean, about 45-50 minutes. Place the pan on a wire rack and cool completely.
For The Icing:
In a medium saucepan, set over medium heat, melt butter.
Add brown sugar (1 cup) to melted butter (1/2 cup) and bring to a boil. Continue to cook, stirring constantly, for 2 minutes.
Pour in milk (2 tablespoons) and return the mixture to a boil.
Remove from heat and whisk in confectioners' sugar (3 cups) and salt (1/4 teaspoon) until smooth and the mixture has thickened.
If icing is too thick to pour on cake, add hot water, a little at a time, until mixture is desired consistency.
Assembly:
Immediately pour the hot icing over the cake, and quickly spread using an offset spatula to cover the entire cake surface. The icing will quickly set.
Sprinkle with chopped pecans and gently press into the icing. Let icing set.
Notes
Raisins:Be sure to soak your raisins in hot water while you’re mixing up the rest of your cake batter. This process will make them nice and plump...so good! Also, if you’re looking to get a little crazy with your applesauce cake, you can soak your raisins in (gasp) hot rum. Pops of flavor throughout!
Sinking! Because this cake is so moist, it might sink in the center. Personally, I don't consider this to be a problem. For me, it's a trade-off. Extraordinary moistness for a little less pretty!