Preheat oven to 350 degrees. Coat a 9×13 pan with cooking spray or the extra coconut oil and line with parchment paper.
Mix together the coconut oil, brown sugar and beat together in with hand mixer or stand mixer until fully incorporated. Add flax egg, applesauce, vinegar, and vanilla extract and mix again until fully combined. In a separate bowl, mix together dry ingredients (flour, salt, baking powder, baking soda, and cinnamon). Add dry ingredients to wet ingredients and combine until fully mixed.
In a separate bowl, mix together all ingredients for crumb topping (should be clumpy) with a fork or your fingers. Put batter in a parchment paper-lined pan and top with crumb topping. Bake for 45-50 minutes. If crumb topping gets too brown, tent with foil. Allow cake to cool.
While the cake is cooling, mix all icing ingredients together in a bowl and drizzle on top of the cake. Let icing set before cutting into squares and serving.
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