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.
Cream Cheese Frosting:
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.