Prepare the Brownie Base: Combine brownie mix, eggs, and melted butter in a medium mixing bowl. Mix, either with a wooden spoon or electric mixer, until smooth. Spread 3/4 of brownie batter into the bottom of prepared pan. Set remaining batter aside.
Prepare the Swirl: Cream the cream cheese until smooth in a small mixing bowl. Add the pumpkin and mix until smooth. Add the egg, granulated sugar, and pumpkin spice. Mix until smooth and well combined.