Preheat oven to 350°F (175°C).
In a mixing bowl, cream together butter and sugar until light and fluffy.
Beat in eggs one at a time, then stir in vanilla.
Combine flour, baking soda, and salt; gradually add to the creamed mixture.
Drop by rounded spoonfuls onto ungreased baking sheets.
Bake for 10-12 minutes, or until edges are golden brown. Cool on wire racks.
For the filling, beat together butter, powdered sugar, vanilla, and milk until smooth and creamy.
Spread filling on the flat side of one cookie, then top with another cookie to make a sandwich.