Preheat your oven to 350°F and line a baking sheet with parchment paper or a silicone baking mat.
In a small bowl, whisk together flour, baking powder, and salt.
In a medium bowl, combine butter and sugar and cream together until light and fluffy, 1 to 2 minutes. Add egg white and vanilla extract and beat until well-combined.
Add flour mixture and beat until mixed. Dough will be fairly soft and sticky.
Place powdered sugar in a small bowl and drop a 1 1/2-ounce spoonful of dough into the powdered sugar. Toss to coat and roll into a ball. Place dough on your prepared baking sheet and repeat with remaining dough. This should make 6 cookies.
Use a flat-bottomed glass or the palm of your hand to smash each cookie dough ball until it is 1/2-inch thick. Bake for 9 to 12 minutes, until cookies look set and the bottoms are lightly golden. Do not overbake.
Allow cookies to cool on the baking sheet until cool enough to handle before transferring them to a cooling rack. Cool completely before frosting.
In a medium bowl, beat softened butter until fluffy. Add powdered sugar, 1 teaspoon of the milk/cream, vanilla, and salt and beat until smooth.
Add milk by the 1/4 teaspoon until frosting reaches your desired consistency. Add a couple drops of food coloring to color if desired.
Use a knife or offset spatula to swirl frosting onto the cooled cookies. Top immediately with sprinkles and enjoy.
*Correct flour measurement is very important in this recipe. For best results, measure by weight or the Spoon and Sweep Method (stir the flour in your container to fluff it up and then spoon it into your measuring cup, sweep excess off with the flat of a knife).