Preheat the oven to 350°F (175°C) and grease a 9x13 inch baking pan.

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

Add the egg and vanilla extract, mixing until well combined.

In a separate bowl, whisk together the flour, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Spread the cookie dough evenly into the prepared baking pan.

Bake for 20-25 minutes, or until the edges are lightly golden and a toothpick inserted in the center comes out clean.

Allow to cool completely in the pan on a wire rack.

In a mixing bowl, beat the softened butter until creamy.

Gradually add the powdered sugar, mixing well after each addition.

Add the milk and vanilla extract, mixing until the frosting is smooth and spreadable.

Once the cookie base is completely cooled, spread the frosting evenly over the top.

Cut into bars and serve.