Preheat the oven to 350°F (177°C). Adjust oven rack to the center rack position. Line a 9×13-inch metal or glass baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out of the pan. Set aside.

Whisk the flour, baking soda, ginger, cinnamon, allspice, cloves, nutmeg, pepper, and salt together in a large bowl. Set aside.

In a medium bowl, whisk the melted butter, brown sugar, granulated sugar, and molasses together until no lumps remain. Whisk in the egg and vanilla. Pour the butter mixture into the flour mixture and mix with a large spoon or silicone spatula until no traces of flour remain. The dough will be thick and shiny. Transfer the dough to the prepared baking pan and press it into a smooth, even layer. It may not seem like enough dough, and it will be a thin layer—that’s OK.

Bake for 23–26 minutes or until the top is set but still looks quite soft and a toothpick inserted in the center comes out mostly clean with only a few moist crumbs. Err on the side of under-baking. Bars puff up in the oven, but settle and firm up as they cool. Allow the bars to cool in the pan set on a cooling rack for at least 1 hour.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and butter together on medium-high speed until smooth, about 2 minutes. Scrape down the sides of the bowl as needed. Add the confectioners’ sugar, ginger, cinnamon, allspice, and vanilla extract. Beat on low speed for 30 seconds, then increase to high speed and beat for 2 minutes until completely combined and creamy. Taste and beat in a pinch of salt if the frosting is too sweet. Spread the frosting on the cooled bars. Top with sprinkles, if desired. To help set the frosting, refrigerate for 30 minutes before slicing and serving.

Lift the bars out of the pan by gripping the parchment paper overhang; transfer to a cutting board and cut into squares. Cover leftover bars tightly and store in the refrigerator for up to 5 days. If you skipped the frosting, cover and store plain gingerbread cookie bars at room temperature for up to 3 days, or in the refrigerator for up to 1 week.