In a mixing bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
Combine the flour, cocoa powder, baking powder, and salt; gradually blend into the creamed mixture.
Drop dough by teaspoonfuls onto ungreased baking sheets.
Bake for 10 to 12 minutes in the preheated oven, until set. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.
To make the frosting, mix together the powdered sugar, milk, and vanilla extract until smooth. Spread over cooled cookies.