Preheat the oven to 350 degrees. Line a 9 x 9 pan with foil or parchment paper.
In a large bowl combine the flour, baking powder, baking soda, cinnamon, and nutmeg. Mix well and set aside.
In another large bowl cream together the butter and sugar. Add in the egg and vanilla and mix well.
Stir in the ginger.
Pour the flour mixture into the butter mixture and mix until combined.
Spread into the prepared pan and bake for 17-20 minutes.
Remove from oven and cool completely on a wire rack.
To make the frosting put the butter and cream cheese in a large bowl and beat on medium high speed until combined.
Add in the vanilla and milk and beat well.
Add the powdered sugar, a half cup at a time, and mix until desired consistency is reached.
Spread the frosting on top of the bars and sprinkle with the sprinkles.
Cut into 16 squares and enjoy!