In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.

Beat in the eggs one at a time, then stir in the vanilla extract until well combined.

In a separate bowl, whisk together the flour, baking powder, and salt; gradually add the dry ingredients to the wet mixture, mixing until just combined.

Divide the dough in half, flatten each portion into a disc, wrap in plastic wrap, and chill for at least 1 hour.

On a lightly floured surface, roll out one disc of chilled dough to about 1/4-inch thickness and cut into desired shapes using cookie cutters.

Place cookies on baking sheets lined with parchment paper and bake at 375°F (190°C) for 8-10 minutes, or until edges are lightly golden.

Let cookies cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.

For the icing, whisk powdered sugar, milk, and vanilla until smooth; optionally add food coloring and decorate cooled cookies with icing and sprinkles.