In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add to the creamed mixture alternately with milk, beating well after each addition.
Drop by rounded spoonfuls onto a greased baking tray.
Bake for 15-20 minutes or until golden brown. Let cool on a wire rack.