Preheat your oven to 350 and line a 9x9 pan with parchment paper.
In a small mixing bowl, combine your dry ingredients (oat flour, baking soda, cinnamon, ginger, allspice, nutmeg, cloves and salt) and stir together.
In a large mixing bowl, combine your coconut oil, brown sugar, and applesauce and blend together well. Add in your molasses and water, and whisk together. Lastly, whisk your egg in.
Pour your dry ingredients into your wet ingredients and stir together till all is well incorporated. Let your cake batter rest for a few minutes for the oat flour to soak up some of the wet ingredients, and your batter will thicken a bit.
Pour your batter into your lined 9x9 pan and bake for 30-35 minutes, or till the top is set and springy, and a toothpick inserted comes out clean.
In a large mixing bowl using a hand mixer, beat your cream cheese for a minute, or till it's creamy. Add in your vanilla and beat together again.
Add your powdered sugar and beat for a couple minutes, till the frosting is smooth and creamy.