1. Preheat oven to 350ºF. Mist an 8-inch square baking pan with cooking spray; line with parchment.
2. Whisk together butter, sugar, eggs, pumpkin puree and vanilla in a large mixing bowl. Stir in baking soda, baking powder, pumpkin pie spice and salt. Stir in 1/2 of flour, then milk, then remaining flour, stirring until just combined (do not overmix). Fold in chocolate chips and nuts.
3. Scrape batter into pan and smooth top with a rubber spatula. Bake until firm to the touch and a toothpick inserted in center comes out clean, 55 to 60 minutes. Let cake cool in pan on a wire rack for 5 minutes, then invert onto rack. Immediately turn right side up onto another rack to cool completely. Cut into 9 squares and serve.