Preheat oven to 350°F. Spray a 9x13 baking dish with non-stick cooking spray.
In a large bowl, cream together the butter, brown sugar, and molasses using an electric mixer.
Beat in the eggs and vanilla.
Stir in the flour, ginger, baking powder, baking soda, and salt until just combined.
Use a rubber spatula to spread the mixture into the prepared baking dish. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
Cool completely before frosting.
To make the frosting, beat together the cream cheese, butter, powdered sugar, and vanilla in a large mixing bowl until smooth and creamy.
Spread frosting over the cooled bars and serve.
Store in the fridge for up to 5 days.