Combine the coconut oil, vanilla, applesauce, and egg in a bowl. Mix well. In another bowl, whisk the sugar, flour, baking powder, baking soda, cinnamon, and salt. Add the wet mixture and mix well. Fold in the zucchini.
Line a square 8 x 8-inch baking pan with parchment. Spread mixture in the pan and bake for 20-25 minutes, until a toothpick inserted in the center comes out clean. Allow to cool completely before cutting into squares.