In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg and maple flavoring until combined. Beat in as much flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Cover dough and chill in the refrigerator about 1 hour or until easy to handle.
Divide dough into eight portions. On a lightly floured surface, roll each portion into a rope 1/2 inch in diameter. Cut ropes into logs about 3 inches long. Place logs on an ungreased cookie sheet.
Bake in a 375 degree F oven for 8 to 10 minutes or until done. Transfer cookies to a wire rack; cool. Spread cookies with Maple Frosting: pull tines of fork through frosting so it resembles bark. Makes 48 cookies.
In a small mixing bowl beat butter for 30 seconds. Gradually add the 1-1/2 cups powdered sugar, beating well. Beat in milk and maple flavoring. Gradually beat in the remaining 1-1/2 to 1-3/4 cups powdered sugar to make spreading consistency.