Preheat oven to 350°F and grease a jelly roll pan.
Beat eggs, sugar, oil, and pumpkin until smooth.
Whisk flour, baking powder, cinnamon, baking soda, and salt in a separate bowl.
Add dry ingredients to pumpkin mixture and mix until combined.
Spread batter evenly in the prepared pan.
Bake until the bars spring back and a toothpick comes out clean.
Cool completely.
Beat cream cheese and butter until smooth.
Add powdered sugar and vanilla and beat until creamy.
Spread frosting over cooled bars and cut into squares.
Notes
Use a jelly roll pan so the bars bake evenly and stay bar-height rather than cake-height. Cool completely before frosting or the cream cheese frosting will melt. Store refrigerated because of the frosting. Make up to a day ahead for easier slicing.