Preheat the oven to 350ºF. Coat a 9x13 baking dish with cooking spray.
In a large bowl, whisk together melted butter and brown sugar. Add eggs and vanilla and whisk until smooth and thick. Fold in squash puree. Add flour, baking powder, soda, and cinnamon and fold with a spatula until the dry ingredients are fully incorporated. Fold in the chocolate chips.
Transfer the dough to the prepared baking pan and smooth the top. Bake in the preheated oven for 24-27 minutes or until the top is set and a toothpick inserted in the center comes out clean or with moist crumbs attached. Allow the cake to cool completely before cutting. Cake will last three days well wrapped at room temperature.