Preheat oven to 350 degrees Fahrenheit. Grease a 9x13 inch pan.
Whisk eggs and pumpkin puree together. Add sugar and whisk to combine. Slowly whisk in oil.
Add flour, baking powder, baking soda, cinnamon, pumpkin pie spice, ginger, and salt. Stir until just combined. Fold in nuts if using.
Pour into prepared pan and spread evenly. Bake 28 to 32 minutes until toothpick comes out clean.
Cool completely on a wire rack — at least 1 to 2 hours.
Beat cream cheese until smooth. Beat in butter. Add powdered sugar in additions, then vanilla and salt. Beat until thick and fluffy. Add cream to thin if needed.
Spread frosting over cooled bars. Refrigerate 30 minutes. Slice into 16 to 20 squares, wiping knife between cuts.