Use an electric hand mixer or stand mixer with a paddle attachment in a bowl. Cream together the butter, granulated sugar, and light brown sugar. Mix on a medium-high speed for about 2 minutes until the mixture becomes lighter in color.
Add in the egg and molasses on a medium speed until combined. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Add in the flour, ginger, cinnamon, baking soda, and salt. Mix on low until just combined. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Using a 3 Tbsp a cookie scoop into 14 cookie dough balls.
Place 6 cookies baking sheets and flattenly slight to more of a disc. Bake at 350 degrees for 11-12 minutes, or until the cookies seem set in the center. Allow to cool on the sheet for 10 minutes, then place on a wire rack to finish cooling.
While the cookies bake and cool, make the frosting. Beat butter in a large bowl with a hand mixer on medium speed in a large bowl for 30 seconds, or until smooth.
Add on the vanilla extract and mix on a medium speed until combined.
Mix in the powdered sugar and milk on a low speed. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Once the powdered sugar is incorporated, mix for an additional minute on a low speed to give the frosting a super smooth consistency.
Spread a thin layer of frosting on top of the cooled cookies using a small offset spatula or butter knife. Top with sprinkles. Makes 14 cookies.