Preheat the oven to 350°F. Butter an 8×8 inch baking pan and line the bottom and sides with parchment paper, leaving some overhang for easy removal later. Set aside.
In a medium bowl, whisk together the sugar and cinnamon for the cinnamon sugar. Set aside.
In another medium bowl, whisk together the flour, cinnamon, pumpkin pie spice, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine the melted butter, dark brown sugar, and granulated sugar. Whisk vigorously for about 1 minute until it forms a paste-like consistency.
Add the egg and egg yolk to the butter mixture and whisk until smooth.
Stir in the pumpkin puree and vanilla extract, mixing to combine.
Gradually add the flour mixture to the wet ingredients and mix until just combined with no visible dry streaks of flour, being careful not to overmix.
Drop half of the batter into the prepared pan and spread it evenly. Sprinkle half of the cinnamon sugar mixture evenly over the top.
Drop small dollops of the remaining batter over the cinnamon sugar layer, spreading gently to cover evenly without disturbing the cinnamon layer beneath.
Sprinkle the remaining cinnamon sugar evenly over the top.
Bake in the center of the oven for 32 to 38 minutes, or until the top is puffed and browned and a skewer inserted into the center comes out clean with a few moist crumbs. The surface will be crisp but will soften as it cools.