Preheat oven to 350 degrees and spray a 9x9 baking dish with pam baking spray.
Using a large bowl, whisk together the flour, baking powder, salt, sugar, cinnamon, nutmeg, and cloves.
Using a medium bowl, whisk the applesauce, milk, melted butter, vanilla, and grated carrots.
Gradually whisk the wet ingredients into the dry ingredients.
Pour the batter into the baking dish.
Using a small bowl, whisk together the sugar, light brown sugar, and chopped walnuts.
Sprinkle over the batter.
Carefully pour the hot water over the top.
Bake in the oven and bake for 45-55 minutes or until the middle is set.
Allow cooling for 10 minutes before serving with ice cream!