Preheat oven to 350°F (177°C) and position rack in the center. Line a 9×13-inch pan with parchment paper with overhang.
Whisk flour, baking soda, ginger, cinnamon, allspice, cloves, nutmeg, black pepper, and salt in a large bowl.
In another bowl, whisk melted butter, brown sugar, granulated sugar, and molasses until smooth.
Add egg and vanilla extract to the wet mixture and whisk well.
Combine wet and dry mixtures and stir until no flour streaks remain.
Press the thick dough evenly into the prepared pan.
Bake for 23-26 minutes until top is set but slightly soft. Let cool in pan for at least 1 hour.
For frosting, beat cream cheese and butter on medium-high until smooth.
Add confectioners’ sugar, ground ginger, cinnamon, allspice, and vanilla; beat on low then high speed until creamy.
Adjust sweetness with a small pinch of salt if needed.
Spread frosting evenly over cooled bars.
Optional: sprinkle decorative sprinkles.
Refrigerate bars for 30 minutes to set frosting.
Use parchment overhang to lift bars, cut into squares.
Store frosted bars covered in the refrigerator up to 5 days or plain bars at room temperature 3 days or refrigerated 1 week.