Preheat the oven according to the temperature specified on the brownie mix package, typically 350°F (175°C).
Lightly grease a 9-inch square baking pan. Line it with parchment paper, leaving some overhang on the sides for easy removal.
Prepare the brownie batter according to the package directions. Fold in the semi-sweet chocolate chips and set aside.
In a large mixing bowl, beat the softened cream cheese with a hand mixer or stand mixer until light and fluffy.
Add the granulated sugar and beat until well combined.
Mix in the egg and vanilla extract until the cheesecake mixture is smooth.
Add the pumpkin puree and pumpkin pie spice. Mix just until evenly combined.
Spread half of the brownie batter evenly over the bottom of the prepared pan.
Spoon the pumpkin cheesecake mixture over the brownie layer. Carefully spread it into an even layer using an offset spatula or the back of a spoon.
Spoon the remaining brownie batter over the cheesecake mixture.
Gently drag the tip of a knife through the layers to create an attractive swirl pattern without completely mixing them together.
Bake the Easy Pumpkin Brownies for 40–45 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs.
Allow the brownies to cool completely in the pan.
Lift them from the pan using the parchment-paper overhang, then cut into squares and serve.