Step 1: Preheat your oven to 350°F (175°C). Line an 8×8 inch baking pan with parchment paper, leaving an overhang on two sides, or grease and flour the pan. Set aside.
Step 2: In a light-colored saucepan, melt the unsalted butter over medium heat. Continue to cook, stirring occasionally, until the butter foams, and little golden brown bits appear at the bottom of the pan. It will smell nutty. This takes about 5-7 minutes. Immediately remove from heat and pour into a large heatproof bowl to cool slightly.
Step 3: To the slightly cooled brown butter, add the light brown sugar and dark brown sugar. Whisk until well combined and smooth.
Step 4: Whisk in the pumpkin puree, large egg, egg yolk, and vanilla extract until the mixture is uniform and creamy.
Step 5: In a separate medium bowl, whisk together the all-purpose flour, cornstarch, pumpkin pie spice, baking powder, and salt.
Step 6: Add the dry ingredients to the wet ingredients. Mix with a rubber spatula until just combined. Be careful not to overmix; a few streaks of flour are okay. If using, fold in the chocolate chips now.
Step 7: Pour the batter evenly into the prepared baking pan. Spread it out gently with the spatula.
Step 8: Bake for 25-30 minutes, or until the edges are set and a toothpick inserted into the center comes out with moist crumbs, not wet batter. The center may look slightly underdone, which is perfect for a fudgy texture.
Step 9: Remove the pan from the oven and let the blondies cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Slice into 16 squares and serve. Store leftovers in an airtight container at room temperature for up to 3 days.