Preheat the oven to 375 °F . Lightly spray a 9x13-inch baking dish with nonstick spray.
In a large bowl, whisk together the eggs, applesauce, ⅓ cup sugar and almond butter. Whisk in the cinnamon, baking soda, salt and vanilla extract.
Stir in the melted butter and milk.
Stir in the uncooked oats.
Stir together ⅓ cup brown sugar and 2 teaspoon cinnamon, and set aside.
Pour the oatmeal into the prepared baking dish
Sprinkle the cinnamon and brown sugar mixture on top, and use a dull knife to swirl it around through the oatmeal.
Bake for 45 minutes until browned around the edges. When the oatmeal is done, a knife or skewer inserted into the center of the oatmeal should come out clean.
While the oatmeal is baking, make the vanilla icing: stir together the Neufchâtel cheese, confectioner's sugar, vanilla extract and milk. Wait until the oatmeal cools a bit after coming out of the oven and evenly spread the vanilla icing over the top.