Preheat oven to 350 degrees. Butter and flour an 8x8-inch cake pan. Set aside.
In a bowl, combine the oats and the boiling water. Cover for around 5 minutes while you assemble the other ingredients.
In a large bowl, whisk together the sugars, flour, salt, baking soda and cinnamon. In a large measuring cup, whisk together the applesauce, egg and vanilla. Add the wet ingredients and the oatmeal mixture to the dry ingredients and fold to combine. Pour into the prepared baking pan. Bake for about 25 minutes or until the center of the cake is set.
Prepare the topping:
In a bowl, combine all of the topping ingredients until well mixed. Immediately upon removing the cake from the oven, turn the oven to broil. Gently spread the topping over the hot cake; broil until the topping is golden brown. Do NOT walk away from the oven during this time - this took less than a minute in my broiler, but may fluctuate based on your oven.