Preheat oven to 350 degrees F (175 degrees C). Spray a large jelly roll pan with cooking spray.
Beat eggs in a large bowl with an electric hand mixer until foamy; add white sugar, vegetable oil, and pumpkin. Beat on medium speed until incorporated, 2 minutes.
Mix flour, baking powder, 2 teaspoons cinnamon, baking soda, and salt in a separate bowl. Beat flour mixture into egg mixture on low speed until just combined, 1 minute. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 25 minutes. Cool completely.
Beat cream cheese, butter, and vanilla together in a bowl with an electric hand mixer until creamy. Gradually add confectioners' sugar; beat until smooth. Spread frosting evenly over cooled pumpkin cake; sprinkle with cinnamon.