Preheat the oven to 350°F and line a 9x15-inch or 9x13-inch baking pan with parchment paper and set aside.
In a large bowl, whisk together the flour, ginger, baking soda, cinnamon, and salt and set aside.
In a separate large bowl or bowl of a stand mixer fitted with a paddle attachment, beat the shortening on low speed and slowly add in the sugar and beat until fully combined, scraping down the sides of the bowl as needed.
Beat in the eggs one at a time, mixing between each addition, then mix in the molasses until incorporated.
Add the flour mixture a little at a time until fully incorporated.
Transfer the dough to the pan and gently press it into the pan.
Bake for 18 to 24 minutes until the edges begin to turn golden and a toothpick inserted into the center comes back clean.
Place the pan on a wire rack to cool completely before frosting.
To make the frosting, beat together the butter, cream cheese, and vanilla until smooth.
Add the powdered sugar a little at a time and mix until the frosting is silky smooth.
Spread the frosting over the top of the cooled bars and top with sprinkles.
Slice the bars into squares.