Using an electric mixer, combine eggs, sugar, oil and pumpkin until light and fluffy. Stir together the flour, baking powder, cinnamon, salt and baking soda. Add the dry ingredients to the pumpkin mixture and mix at low speed until thoroughly combined and the batter is smooth. Spread the batter into a grease baking pan (13x10). Bake for 30 minutes. Let cool completely before frosting.
Combine the cream cheese and butter with an electric mixer until smooth. Add the sugar and mix at low speed until combined. Sir in the vanilla and mix again. Spread on cooled pumpkin bars.