Preheat oven to 350°F (175°C) and grease or line a 9x13-inch pan.
Whisk flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt in a bowl.
In another bowl, beat sugar and oil until smooth, then mix in eggs one at a time and stir in pumpkin purée.
Add dry ingredients to wet, stirring just until combined to keep the bars soft.
Spread batter evenly in the pan and bake 25–30 minutes until a toothpick comes out clean.
Cool completely on a wire rack before adding the drizzle.
Beat cream cheese and butter until smooth, then mix in powdered sugar, vanilla, pumpkin spice, and milk until pourable.
Drizzle over cooled bars, slice into squares, and serve once the topping sets slightly.