In the bowl of a stand mixer, cream sugar and butter until light and fluffy, about 2 minutes on medium-high. Add vanilla extract, almond extract and the whole egg. Mix, then add the egg white and mix until combined.
In a small mixing bowl whisk together flour, baking powder and salt. With mixing speed on low, gradually add dry ingredients until no flour pockets remain. I like to roll the dough out between two sheets of plastic wrap so that it's just under 1/2" thick, stick it on a baking sheet and refrigerate for 2-3 hours (that way I can just remove the plastic wrap and cut my first set of cookies out). You can also place the dough in an airtight container and refrigerate as well.
Preheat oven to 375 degrees. Line two baking sheets with parchment paper or baking mats, set aside.
Roll dough out on a floured surface to just under 1/2" thick. Cut cookies and transfer to prepared baking sheet, place at least 1/2" apart (or cut directly from the rolled sheet of dough).
Place in oven and bake for 8-10 minutes (the cookies will look extra soft, do not over bake) or until the cookies become firm on the edges. Remove and allow to cool for 3 minutes before transferring to a wire rack to cool completely. Re-roll dough and continue cutting and baking until all of the dough has been used.
Meanwhile, to make the frosting, in the bowl of a stand mixer cream butter until it becomes light and smooth. Add salt, 2 tablespoons of milk and vanilla. With mixing speed on low gradually add powdered sugar. Once powdered sugar is incorporated, bring mixing speed up to high and beat for 2 minutes. Add more milk to reach the desired consistency. Frost onto cooled cookies and top with desired sprinkles.