Instructions

Make the cookies:

1. Using an electric mixer on medium speed, beat the butter and sugar until light and fluffy. Add the egg yolks and vanilla extract, and mix well.
2. Reduce the mixer speed to low, and gradually add the flour. Mix just until combined. The dough will be crumbly. Use your hands or a mixing spoon to finish mixing until the a dough forms.
3. Cover and refrigerate the dough for 1 hour.
4. Preheat the oven to 375°F. Line baking sheets with parchment paper or silicone liners.
5. Using a tablespoonful of dough at a time, roll the dough into smooth balls. Place on the prepared pans, leaving about 2 inches between the cookies. Use your thumb, the handle of a wooden spoon, or a small round measuring cups to make an indentation in the center of each cookie dough ball. (Dip whatever implement you're using into flour or just dampen with water if the dough is sticking.)
6. Bake one pan at a time for 10 to 12 minutes, or until the cookies are golden brown. Refrigerate the remaining dough between batches.
7. Place the pans on wire racks, and allow the cookies to cool for 5 minutes before transferring them from the pans directly onto a wire rack to cool completely. If necessary, use a spoon handle or a measuring spoon to remake the indentations in the cookies when they come out of the oven.

Make the frosting:

1. Using an electric mixer on medium speed, beat the butter and confectioners' sugar until combined. Add 1 tablespoon of the milk and the vanilla, and mix until combined and smooth. If necessary, mix more milk into the frosting until it reaches the desired consistency.
2. Fill the cooled cookies with frosting, and top with sprinkles.