4 ounces (half an 8-inch block) cream cheese, at room temperature
4 tablespoons unsalted butter, at room temperature
1 1/2 cups confectioners’ sugar
1 teaspoon vanilla extract
Place a rack in the center of the oven, and preheat the oven to 350 degrees F. Mist a 13- by 9-inch pan with vegetable oil spray, and set the pan aside.
Place the pumpkin, eggs, granulated sugar, brown sugar, and oil in a large mixing bowl, and mix with a wooden spoon until the eggs are incorporated and the mixture has thickened slightly and is smooth, about 100 strokes. Place the flour, pumpkin pie spice, baking soda and salt on top of the pumpkin mixture, and with a fork, toss the dry ingredients together to combine lightly. Using the wooden spoon, fold the dry ingredients into the pumpkin mixture and stir until smooth, about 50 strokes.
Turn the batter into the prepared pan, and place the pan in the oven. Bake until the cake springs back when lightly pressed and has turned lightly browned around the edges, 25 to 30 minutes. Remove the pan from the oven to cool.
Meanwhile, prepare the icing. Place the soft cream cheese and butter in a medium-size mixing bowl. Blend with a hand-mixer on low speed, or with a wooden spoon, until smooth. Add the sugar and vanilla, and blend until smooth, 1 minute.
When the pumpkin cake has cooled to the touch, spread the icing over the top of the cake, and let the cake rest for 1 hour before slicing into squares or bars.