Sift together 3 1/4 cups flour, baking powder, and salt. Set aside.

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

Beat in eggs one at a time.

Stir in vanilla extract.

Gradually blend in the sifted dry mixture until fully absorbed.

Form dough into ball and place on top of plastic wrap. Wrap the dough with the plastic wrap.

Chill dough for at least 2 hours.

Preheat oven to 350°.

Prepare cookie sheets by lightly greasing them or use parchment paper.

Using the reserved 1/2 flour, sprinkle some on a clean surface.

Roll out small portions of chilled dough to 1/4 inch thickness. Cut out shapes using cookie cutters. Place cookies on cookie sheet.

Bake 8-12 minutes, or until edges are barely brown. Remove from cookie sheets to cool on wire racks.

In a large bowl, cream together the confectioners' sugar and butter until smooth. 

Gradually mix in the milk and vanilla with an electric mixer until smooth.

Add food coloring if desired.

Ice cookies and top with sprinkles if desired.