Preheat oven to 350°F (180°C). Grease and line a 9 x 9-inch baking pan with parchment paper.
In a large bowl, whisk together flour, baking powder, baking soda, and pumpkin pie spice. Set aside.
2 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 teaspoon pumpkin pie spice
In another bowl, whisk the eggs, oil, brown sugar, granulated sugar, pumpkin purée, milk, and vanilla until smooth.
3 large eggs, ⅔ cup vegetable oil, 1 cup brown sugar, ¼ cup granulated sugar, 2 cups pumpkin purée, ¼ cup whole milk, 2 teaspoons vanilla extract
Add the dry ingredients to the wet mixture and stir until just combined.
Pour the batter into the prepared pan and spread evenly. Bake for 25–30 minutes, or until the center springs back when lightly pressed.
In a bowl, beat the cream cheese until smooth. Add powdered sugar and vanilla extract, then beat until creamy. Spread frosting evenly over the cooled cake and dust lightly with cinnamon if desired.
1 cup cream cheese, 1 teaspoon vanilla extract, 1 cup powdered sugar