Preheat oven to 350 and lightly grease (even if using parchment paper) an 8x8 baking dish. In a small bowl, stir flaxseed and warm water together and set aside for a few minutes.
In a large bowl, whisk dry ingredients: flour, pumpkin pie spice, baking powder, baking soda, and salt.
In a medium bowl, stir together wet ingredients: flaxseed mixture, pumpkin puree, coconut oil, maple syrup, and vanilla extract.
Pour wet mixture into the dry ingredients and stir to combine. Batter will be thick! Spread into prepared dish and bake for 25 minutes or until a toothpick comes out clean. Set aside and let cool completely before frosting!