For cookies, combine flour, sugar, cocoa powder and salt in large bowl. In small bowl, cream butter. Add eggs, 1 at a time, beating until well mixed. Beat in vanilla. Stir into dry ingredients. Form into 4 rolls. Wrap in foil and chill for at least 2 hours.
Preheat oven to 350 degrees.
Slice rolls thinly. Bake for 5 minutes (no longer). Cool on a wire rack.
For filling, beat butter, cream cheese, milk and vanilla in medium bowl. Beat in confectioners’ sugar. Spread filling on half of cooled cookies and top with remaining cookies, pressing slightly to adhere to filling.