Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper.
In a mixing bowl, combine the flour, baking powder, and salt. Set aside.
In another large mixing bowl, cream the softened butter and granulated sugar until light and fluffy using an electric mixer or whisk.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the butter mixture, mixing until a soft dough forms.
Roll the dough out on a lightly floured surface to about ¼-inch thickness. Use cookie cutters to cut out shapes of your choice.
Place the cookies on the prepared baking sheets, about 2 inches apart. Bake for 8-10 minutes, or until the edges are lightly golden.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely.
To make the icing, mix the powdered sugar and milk in a bowl until smooth. Divide the icing into bowls and color with food coloring as desired.
Decorate the cooled cookies with the icing and sprinkles. Allow the icing to set before serving.