Preheat oven to 350 degrees. Butter a 9x13-inch baking dish and line with parchment paper letting the edges of the paper extend over the sides for easy removal.
In a medium bowl, whisk together flour, cocoa powder, ginger, cinnamon, baking soda, cloves, nutmeg, and black pepper.
In a large bowl, whisk together butter, dark brown sugar, molasses, sour cream, and eggs until combined really well.
Gradually stir the flour mixture into butter mixture until no lumps or streaks remain. Pour into prepared pan.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean. Let cool in pan for 5 minutes and then remove to a wire rack to cool completely.
For frosting, beat cream cheese and butter at medium speed with an electric mixer until light and fluffy. Beat in vanilla extract, salt, and cinnamon.
Add confectioners' sugar 1/2 cup at a time, turning speed down to low with each addition and then back up to medium to combine well. Beat in brown sugar.
Spread frosting on cake and serve immediately or refrigerate for up to 5 days.