Preheat oven to 375°F (190°C).

In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the egg and vanilla extract.

Gradually add the flour, mixing until just combined.

Roll out the dough on a lightly floured surface to 0.25 inch thickness. Cut out shapes using cookie cutters.

Place cookies on ungreased baking sheets and bake for 8-10 minutes, or until edges are lightly golden.

Let cookies cool on baking sheets for a few minutes before transferring to a wire rack to cool completely. Frost and decorate as desired.

In a medium bowl, whisk together powdered sugar, milk, and vanilla extract until smooth. Add food coloring, if desired.