Preheat the oven to 350°F. Line an 8x8 baking dish with parchment paper or spray it lightly with cooking spray.
Whisk together the flour, baking powder, baking soda, cinnamon, and salt in a medium mixing bowl.
In a large mixing bowl, whisk together the sugar, oil, vinegar, vanilla, and milk.
Pour the dry ingredients into the wet ingredients and stir until just combined. Do not overmix!
Add in the shredded zucchini and chocolate chips and stir gently to incorporate evenly.
Transfer the batter to the prepared baking dish and smooth out the top. Bake for 30 to 35 minutes until a toothpick inserted in the center comes out clean. (If the toothpick comes out with melted chocolate, that's fine and expected, but no batter should be on the toothpick).
Let cool in the pan on a cooling rack before removing and cutting into squares.
Drizzle the chocolate sauce, if using, over the top of the pieces of cake.