Heat oven to 350°F. Grease and line a 9x13-inch pan with parchment.
Whisk flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves in a bowl.
Beat granulated sugar, brown sugar, and eggs until slightly thick and lighter, about 2 minutes.
Mix in oil, pumpkin puree, and vanilla until smooth.
Fold dry ingredients into the pumpkin mixture just until no flour streaks remain.
Spread batter evenly in the pan and smooth the top.
Bake 25–30 minutes, until a tester comes out clean. Cool completely in the pan.
Beat softened cream cheese and butter until creamy and lump-free, about 2 minutes.
Add confectioners' sugar, vanilla, and salt. Beat on low, then increase speed; add milk to reach a fluffy, spreadable frosting.
Spread frosting over cooled bars. Chill 15 minutes for cleaner cuts, then slice into squares.