Preheat your oven to 350°F (175°C). Lightly grease a jellyroll pan (around 14"x10") or a 9"x13" baking dish with nonstick spray.
In a big mixing bowl, whisk together the Bisquick, granulated sugar, ground cinnamon, and pumpkin pie spice until they're nicely combined.
Pour in the pumpkin puree, milk, eggs, and vegetable oil. Start mixing on low speed until everything just comes together, then scrape down the sides of the bowl. Increase the speed to medium and mix until your batter is smooth and lump-free.
Spread the batter evenly into your prepared pan. Bake for 22-26 minutes (or 30-35 minutes if using a 9"x13" pan), or until a toothpick poked into the center comes out clean. Let the cake cool completely on a wire rack. This is super important before frosting!
While your cake cools, grab a small bowl. Beat the softened butter and cream cheese together with an electric mixer until they're smooth and creamy.
Gradually add the powdered sugar, about 1/2 cup at a time, beating well after each addition until the frosting is smooth. Finally, stir in the vanilla extract until it's light and fluffy.
Once the pumpkin cake is completely cool, spread the delicious cream cheese frosting evenly over the top. Slice into squares and get ready to enjoy these delightful autumn bars!