Preheat your oven to 350°F. In a large mixing bowl, whisk together eggs, sugar, oil, and pumpkin until smooth and well combined.
In a separate bowl, sift together flour, cinnamon, baking powder, baking soda, and salt. Gradually fold the dry ingredients into the pumpkin mixture until just blended.
Spread the batter evenly into an ungreased 15x10x1-inch baking pan. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool completely in the pan on a wire rack.
For the frosting, beat cream cheese, confectioners' sugar, butter, and vanilla extract in a bowl until creamy. Add milk as needed to reach a spreadable consistency.
Once the bars are cool, spread the frosting over the top. Cut into squares and serve. Keep any leftovers refrigerated.