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 dark 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
Soak Those Raisins. Don’t skip the soak! Plumped raisins stay soft and juicy instead of pulling moisture from the cake.
Don’t Overmix. Once you add the flour, mix just until everything is combined. Overmixing can make the cake dense instead of soft and tender.
Have the Cake Ready for Icing. The brown butter icing sets quickly, so make sure your cake is completely cooled and ready before you start making it. Pour and spread the icing immediately.
A Little Sinking Is Normal. This is an incredibly moist cake, so it may sink slightly in the center as it cools. That’s perfectly normal and won’t affect the deliciously tender texture.