Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking dish. Line the dish with parchment paper, letting paper hang over the sides of the dish for easy removal of the brownies.
In a medium bowl, whisk together the flour, cocoa powder, ginger, baking soda, cinnamon, allspice and nutmeg. In a large bowl, whisk together the brown sugar, melted butter, molasses, sour cream and eggs. Slowly stir in the flour mixture a little at a time, stirring just until no lumps or streaks remain. Pour the batter into the prepared baking dish.
Bake until a toothpick inserted into the center of the gingerbread comes out clean, 30 to 35 minutes. Allow the gingerbread to cool in the pan 5 to 10 minutes, then remove by lifting both sides of the parchment paper. Place on a wire rack to cool completely.
Once cool, spread with the Cream Cheese Frosting. Store in an airtight container for up 5 days. Cut into squares and serve, or give as gifts.
In the bowl of an electric mixer, combine the cream cheese and butter and beat until light and fluffy. Beat in the vanilla and salt. Beat in the confectioners' sugar a little at a time, beating until fully incorporated. Use immediately, or refrigerate up to 5 days.