Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add to the butter mixture, mixing until just combined.
Roll the dough into small balls and place them on the prepared baking sheet. Flatten each ball slightly.
Bake for 12-15 minutes, or until the edges are lightly golden. Let cool on a wire rack.
For the icing, mix together the powdered sugar, milk, and vanilla extract until smooth. Dip the tops of the cooled cookies into the icing and decorate with sprinkles.