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Preheat oven to 350.
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Using an electric mixer at medium speed, beat the eggs, granulated sugar, oil, and pumpkin until light and fluffy.
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Sift together the flour, baking powder, cinnamon, salt, and baking soda in another bowl.
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Gradually add the dry ingredients to the pumpkin mixture with the mixer at low speed.
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Mix until thoroughly combined and the batter is smooth.
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Spread the batter in an ungreased 13x9" baking pan.
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Bake for 30 minutes.
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Remove from the oven and let cool completely before frosting.
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To make the frosting: Combine the cream cheese and butter in a medium bowl with an electric mixer until smooth.
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Add the vanilla.
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Slowly beat in the confectioners' sugar until smooth.
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Spread on the cooled pumpkin base and cut into bars.
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These freeze well (as if you're going to have any leftovers).