Preheat oven to 350°F (175°C).
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs and vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until combined.
Drop spoonfuls of dough onto a baking sheet.
Bake for 12-15 minutes or until edges are golden brown.
While cookies cool, mix powdered sugar, milk, and vanilla extract to make the icing.
Once cookies are cool, drizzle icing over the top.