Preheat oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with aluminum foil with about 1 inch hanging over the edges for 'handles'. Spray foil with cooking spray.
Beat brown sugar and butter together in a bowl with an electric mixer until smooth; beat in 2 eggs until combined. Beat 1 more egg and vanilla extract into brown sugar mixture until combined. Stir flour and baking powder together in a separate bowl; stir into brown sugar mixture until batter is smooth.
Beat cream cheese in a separate bowl with an electric mixer until smooth; beat in remaining 1 egg until just combined. Beat pumpkin puree into cream cheese mixture; stir in pumpkin pie spice.
Spread 2/3 the batter into the prepared baking pan. Drop spoonfuls of pumpkin mixture over batter; top with spoonfuls of remaining 1/3 batter and swirl together with a butter knife.
Sprinkle cinnamon chips over batter-pumpkin mixture.
Bake in the preheated oven until blondies are lightly browned on the edges, about 30 minutes. Cool completely before cutting into bars.
