Preheat oven to 350°F. Line a 9×13-inch baking pan with parchment paper.
Cream softened butter, granulated sugar, and brown sugar together.
Add molasses, egg, and vanilla. Mix until combined.
In a separate bowl, whisk flour, baking soda, ginger, cinnamon, nutmeg, and salt.
Gradually combine dry and wet ingredients to form a thick dough.
Press dough evenly into the prepared baking pan.
Bake for 18–20 minutes until edges are set. Cool completely.
Beat cream cheese and butter until smooth.
Add powdered sugar and vanilla, beating until fluffy.
Spread frosting over cooled bars, decorate with sprinkles, and cut into 16 pieces.